Xavier Zambrana-Puyalto

Nicolas Bonod
email: nicolas.bonod@fresnel.fr

Tailoring the chirality of light emission with spherical Si-based antennas

Chirality of light is of fundamental importance in several enabling technologies with growing applications in life science, chemistry and photodetection. Recently, some attention is being focused on chiral quantum emitters. Consequently, optical antennas which are able to tailor the chirality of light emission are needed. Spherical nanoresonators such as colloids are of particular interest to design optical antennas since they can be synthesized at large scales and they exhibit good optical properties. Here, we show that these colloids can be used to tailor the chirality of a chiral emitter.

To this purpose, we derive an analytic formalism to model the interaction between a chiral emitter and a spherical resonator. We then compare the performances of metallic and dielectric spherical antennas to tailor the chirality of light emission. It is seen that, due to their strong electric dipolar response, metallic spherical nanoparticles spoil the chirality of light emission by yielding achiral fields. In contrast, thanks to the combined excitation of electric and magnetic modes, dielectric Si-based particles feature the ability to inhibit or to boost the chirality of light emission. Finally, it is shown that dual modes in dielectric antennas preserve the chirality of light emission.

INTRODUCTION

Optical antennas can resonantly interact with light to enhance the decay rates and to control the directivity of emission of quantum emitters, or reciprocally to enhance the near fields. They have been successfully used for example in molecular spectroscopy [1,2], single photon sources [3][4][5] and photo-detectors [6]. A lot of efforts have also been devoted to design optical antennas which are able to enhance chiral lightmatter interactions. Among recent achievements, we find enhancing the resolution of the circular dichroism technique [7]; controlling the optical rotation of light [8]; creating chiral optical fields from linearly polarized plane waves [9,10]; creating complex chiral plasmonic structures [11][12][13][14][15]; or even digging in the interplay between the angular momentum (AM) of light and chirality [16][17][18][19][20][21][22].

Here we investigate the interaction between a chiral dipolar emitter [23,24] and a spherical optical antenna.

Emphasis is placed on spherical nanoparticles since they can be fabricated at large scales via colloidal synthesis or laser ablation with excellent surface and optical properties [25][26][27][28][29]. The question that we address is whether individual spherical nanoparticles can be used to produce strong chiral effects when interacting with chiral emitters. More precisely, we aim at studying how the antenna modifies the chirality of the emitted field in the far-field region. For that purpose, we present a simple formalism to analyze the chirality of the scattered light. This formalism, which is analytic and valid for antennas of any size, is developed using the Mie theory in the helicity basis [30][31][32]. The formalism is first applied to plasmonic antennas composed by gold spherical nanoparticles [33][34][35], and secondly to dielectric spherical resonators made of silicon [28,29,[36][37][38]. It will be demonstrated that the interplay between electric and magnetic modes of the optical antennas is required to tailor the chirality of light in the far field. In addition, it will be seen that the dual behavior of the particle [30,31,39] plays a very important role.

CHIRAL DIPOLAR EMISSION

At the level of macroscopic Maxwell equations, we consider that a dipolar emitter C is chiral if and only if its emission is described as a superposition of both electric and magnetic dipolar fields. In contrast, we consider that the emitter is non-chiral if its emission pattern is symmetric under at least one mirror symmetry plane. In particular, the field described by either either an electric or a magnetic dipolar field alone are nonchiral. It is also assumed that an emitter whose emitted electromagnetic (EM) field is a combination of electric and magnetic dipolar fields has both electric and magnetic dipole moments, p and m. Note that for chiral emitters, p must be a real magnitude, and m must be imaginary [40] [41, p187].

The description of the EM fields in terms of electric and magnetic multipoles has been proven to be very useful for a huge variety of phenomena. However, for chirality and optical activity studies [START_REF] Fernandez-Corbaton | [END_REF][43][44], a change from the electric/magnetic (or parity) basis to the helicity +1/ -1 basis [32,45] allows for an easier description of the problem. The change from the parity to the helicity basis is made in the following way.

Let A (e)

jmz , A (m) jmz be electric and magnetic multipoles. Then, their linear combinations yield multipolar fields of well-defined helicity [30,32,46]:

A + jmz = A (m) jmz + iA (e) jmz √ 2 A - jmz = A (m) jmz -iA (e) jmz √ 2 (1)
As a result, A + jmz and A - jmz are eigenstates of the helicity operator Λ [39,46]:

ΛA + jmz = +A + jmz ΛA - jmz = -A - jmz (2)
Notice that for both families of multipoles, the sub-indexes j, m z stand for the eigenvalues of the operators (J 2 ) and (J z ) [32]. Now, in the same way that a current density j can be given by an electric or magnetic dipolar moment (p or m), it can also be given by a helicity ±1 dipolar moment (p + or p -) [47].

In Figure 1, we show the emitted fields of the emitter |E C | 2 for two different orientations of p + and p - corresponding to m = 0, +1 (or alternatively ẑ and (x + iŷ)/ √ 2). As it can be observed, the radiation pattern of p + and p -for m = 1 are counter-intuitive, as they are highly directional. This contrasts with the highly non-directional radiation patterns of electric and magnetic dipoles. Nonetheless, the pattern can be inferred from the definition of helicity and its relation to the AM of light [30,39].

Then, we will define the chirality (C) of the emitter as the comparative strength of p + and p -. That is, if the emitted field by the emitter is given by

E C = αA + 1,mz + 1 -|α| 2 A - 1,mz
, then we will define C as: where |α| 2 is the probability that the emitter shines light with helicity +1. As a result, the probability that the emitter emits light with helicity -1 is (1 -|α| 2 ). Using the definition given by eq.( 3), the chirality of the emitter C(α) will be a value going from [-1, +1]. It can be seen that C(α) = +1 indicates that the emitter emission is only given by p + ; C(α) = 0 means that the probability of inducing p + and p -is the same -this is the case of an emitter which is purely given by p or m; finally, C(α) = -1 indicates that the emission is only given by p -. The same definition of chirality will be used to quantify the chirality of the scattered light in the far field.

C(α) = |α| 2 -(1 -|α| 2 ) |α| 2 + (1 -|α| 2 ) = 2|α| 2 -1 (3) 3
In this section, we provide analytic tools to easily describe the chirality of the field scattered off a spherical antenna when the latter is coupled to a chiral emitter. Without any loss of generality, it is assumed that the chiral emitter is located in the z axis and emits light at a unitary rate. We suppose that the chirality of the emitter, given by C(α), is an inherent property. Then, we analytically compute the chirality of the scattered field (C s (α)) as a function of α, the distance between the emitter and the antenna, and the size of the antenna. The theoretical details to compute C s (α) are given in Appendix A, but the general idea can be summarized as follows. The chiral source emits a dipolar field which is a superposition of two dipolar fields with opposite well-defined helicities:

E C = αA + 1,mz + 1 -|α| 2 A - 1,mz
, where m z has to do with the orientation of the emitter. The reference frame of the problem is not located at the center of the emitter, but rather at the center of the antenna. Thus, the translation-addition formulas need to be used to find an analytic expression of the emitted chiral field. Then, the Mie theory in the helicity basis [30][31][32] is used to find the scattered field E s . This scattered field has, in general, two helicity components which contribute separately to the total scattered power. That is, the total scattered power W s is computed as

W s = W s + + W s -,
with W s + , and W s -being the scattered power into modes with helicity +1 and -1, respectively. Then, following the definition of C(α) given by eq.( 3), we compute C s (α) as:

C s (α) = W s + -W s - W s + + W s - (4)
As a result, the chirality of the scattered field by the antenna can be analytically expressed as (see Appendix A):

C s (α) = j ,L |α T j ,L,1,mz a j + b j √ 2 + 1 -|α| 2 T j ,L,-1,mz a j -b j √ 2 | 2 -|α T j ,L,1,mz a j -b j √ 2 + 1 -|α| 2 T j ,L,-1,mz a j + b j √ 2 | 2 j ,L |α T j ,L,1,mz a j + b j √ 2 + 1 -|α| 2 T j ,L,-1,mz a j -b j √ 2 | 2 + |α T j ,L,1,mz a j -b j √ 2 + 1 -|α| 2 T j ,L,-1,mz a j + b j √ 2 | 2 (5)
Note that C s (α) is a multi-variable function and depends upon different parameters apart from α. Naturally, it depends on the features of the emitter such as its emitting wavelength λ 0 , its orientation m z , and its distance to the particle r 0 . In addition, C s (α) depends on some parameters of the antenna such as its radius R, its permittivity and permeability µ.

λ (µm) Q s - d) R=40nm R=60nm R=80nm R=100nm R=40nm R=60nm R=80nm R=100nm R=40nm R=60nm R=80nm R=100nm R=40nm R=60nm R=80nm R=100nm FIG.

GOLD PLASMONIC ANTENNA

Let us first study the chirality properties of the field scattered by a plasmonic antenna made of gold, with µ = 1 and given by a linear interpolation of the data points in [START_REF] Palik | Handbook of optical constants of solids[END_REF]. Four different radius of spherical antennas will be considered, R = 40, 60, 80, 100 nm. We consider a chiral dipolar emitter with |α| 2 = 0.9, emitting from the visible to the near-infrared λ ∈ [400, 900]nm, and located at a constant distance of 10nm along the z axis from the surface of the gold particle. The orientation of the emitter for both helicity components is assumed to be along the z axis, i.e. p + = p + ẑ, and p -= p -ẑ. This orientation passes on to eq.( 5) as m z = 0. It has been numerically verified that this choice of orientation does not affect the results in a qualitative manner.

The spectra of C s (α, R) are displayed in Fig. 2a) for the four different particle diameters. Each of the four subplots of Fig. 2a) displays C s ( √ 0.9, R) as well as the initial chirality of the emitter, C( √ 0.9) = 0.8. It is observed that the chiral behavior of the antenna is almost flat in the whole spectrum and that C s ( √ 0.9, R) ∼ 0 for the four sizes and for the whole spectral range. Moreover, this behavior is completely independent of the resonant behavior of the particle. In Fig. 2b), we plot the efficiency factors Q s [START_REF] Bohren | Absorption and scattering of light by small particles[END_REF] and observe that despite the different spectral resonances in Q s depicted in Fig. 2b), their chirality behavior is almost identical and constant to C s ( √ 0.9, R) ∼ 0. Now, due to the definition of C s (α) (see eq.( 4)), this implies that both helicity components of the scattered field are almost equal. Actually, this feature could have been predicted

beforehand, as it is well known that a gold nanoparticle approximately behaves as an electric dipole. Now, an electric dipole has a 50% -50% decomposition into dipolar fields of two different helicities [START_REF] Zambrana-Puyalto | [END_REF]51]. This fact can be directly deduced from eq.( 1). Hence, it is clear that an electric dipolar particle such as a gold nanoparticle is not a good candidate to enhance the far-field chirality signal of a chiral light emitter.

Figures 2c) andd) show the scattering efficiency factor Q s split into its two helicity components,

Q s = Q s + + Q s -(see Appendix A).
That is, if we add the values from the plots in Figs.2c) and d), we obtain the plots of Figure 2b). Because the nanoantenna almost behaves as an electric dipole, it can be observed that Q s + and Q s -almost yield the same result. Nonetheless, the unitary emission of the chiral emitter, which is modeled by a black line both in Figure 2c) and d), is mostly done (with a probability of |α| 2 = 0.9) in the +1 helicity state; the emission in the -1 helicity state happens with a probability of (1 -|α| 2 = 0.1). Hence, the nanoantenna clearly increases the relative strength of the helicity -1 component, whereas it decreases the strength of the other component. In other words, what a gold nanoantenna does is transforming a big amount of the main helicity state (+1 for this case) of the incident light into the opposite helicity state (-1 in this example).

SI-BASED MIE ANTENNA

We now aim at studying whether Si-based spherical particles hosting electric and magnetic modes are a valuable alternative to plasmonic antennas for tailoring chiral light emission. In Fig. 3 (in blue, left y-axis), we plot C s (α) for a Si nanoantenna of radius R = 40, 60, 80, 100nm using Eq.( 5). The properties of the emitter are the same as those used in the previous section. Note that even though this choice of sizes might seem restrictive, it is demonstrated in Appendix B that Si-based antennas achieve their full potential chirality within this regime. The chirality response of the Si nanoantenna displayed in Fig. 3 contrasts with the rather constant behavior observed with gold particles. It can be observed that coupling a chiral emitter with a spherical silicon particle almost covers the whole range of chirality values for the EM field: the antenna can boost, preserve or even invert the chirality of the emitted fields. However, even if the antenna offers all these possibilities, the scattered power is not constant throughout the spectral range. For this reason, we have also depicted Q s in Fig. 3 (in red, right y-axis). In particular, it is seen that the spectral position of the absolute minimum of C s (α) always coincides with a local minimum of Q s . This effect is specially prominent for the particles with R = 80, 100nm. The underlying reason is an almost null scattered field E s in these two cases.

Hence, due to the definition of C s (α) given by Eq.( 4), small variations of the helicity components W s + and W s -around a zero value can certainly account for great variations. Notice that when C s (α) < 0 and specially when C s (α) ∼ -C(α), the antenna mostly scatters light with the opposite chirality. This was defined in [30][31][32] as an anti-dual behavior. However, we observe that this non-trivial behavior comes with a price: the scattered power is highly reduced.

Another interesting feature of these Si-based antennas is that they can reach C s (α) 1. That is, they can almost scatter all the light in only one helicity component. To unveil the physical process, we plot in Fig. 4 C s (α), Q s , Q s + and Q s -for a Si-based antenna of R = 100nm. The other parameters are the same as they were in Fig. 3. For Fig. 4c)d), a black straight line is plotted to represent the probability to observe light emitted in a ±1 helicity state. Now, Fig. 4d) unveils that the absolute maximum of C s (α) occurs for a non-trivial minima of the initial small helicity component (thecomponent for this example). That is, C s (α) yields the purest chiral state when the energy scattered in thehelicity component is minimum.

It is also worth commenting that, even though the emitter emits with a probability of (|α| 2 = 0.9) in the +1 helicity component, and with a probability (1 -|α| 2 = 0.1) in the -1 component, Q s + and Q s -have a similar spectral behavior (see Fig. 4c) and d)). The underlying reason is that the resonances of a dielectric Mie antenna are of either electric or magnetic nature, and electric/magnetic modes split 50% -50% into modes of both helicities. Thus, every time that Q s reaches a maximum at the excitation of an electric or a magnetic mode, that maximum value passes on to Q s + and Q s - [START_REF] Zambrana-Puyalto | [END_REF]51]. For these cases, the dielectric antenna renders an achiral behavior, i.e. C s ( √ 0.9) ∼ 0. Nonetheless, looking at C s in Figure 4, it can be observed that the antenna can also render an achiral behavior off resonance. In this latter case, the achirality stems from a non-trivial condition on the different modes.

Another feature that can be observed in Fig. 4 is that C s (α) = C(α) for some special wavelengths. At these wavelengths, the scattered field maintains the exact chirality as the emitter. In other words, the antenna becomes transparent to the helicity of the emitted field. Let us note that the cause of this phenomenon is not always the same. For some cases, the particle does not modify the helicity content of an emitter because the particle is dual. Dual particles, by definition, preserve the helicity of light [8,30,31,39,43,53]. In the macroscopic approximation of Maxwell equations, a single sphere embedded in air is dual if and only if = µ.

However, as it is discussed in [31], an approximate dual condition can be found for certain wavelengths by computing the minimum of an intrinsic helicity transfer function defined as [31,32] :

T (R, , µ) = j |a j -b j | 2 j |a j + b j | 2 (6)
The logarithm of the transfer function for the antenna in consideration (R = 100nm, silicon-made) log 10 T (R, , µ) -1 is plotted in Fig. 5(b) and is compared with C s (α, R, λ) plotted in Fig. 5(a). It can be seen that both functions have similar features but they are spectrally shifted. It is also observed that the antenna is only dual for λ ≈ 841nm, which corresponds to an almost zero of T (R, , µ). This λ clearly coincides with one of the intersection points between C s (α) and C(α) in Fig. 5. Nonetheless, the other intersection of C s (α) and C(α) in Figure 5 at λ ∼ 780nm does not correspond to a dual condition. That is, the condition C s (α) = C(α) can also occur without achieving duality. Yet there is a fundamental difference between the two C s (α) = C(α) conditions (dual and non-dual). The dual condition is an intrinsic property of the antenna, whereas the other one is not. That is, the wavelength at which the non-dual C s (α) = C(α) condition occurs depends on the emitter properties, such as the parameter α. In contrast, the dual condition is fixed by the geometry and material of the antenna.

Since available mono-disperse colloidal solutions have 2% standard deviations [26], it is important to check if these changes in size could potentially spoil the behavior of the antenna. To verify that, we set out to study the value of C s (α) for a radius of R = (100 ± 2)nm around λ = 808nm, i.e. the wavelength at which C s (α) has a maximum for R = 100nm. The results are depicted in Fig. 6. It is observed that the chirality of the emitter is boosted for all the radius in the interval. Now, if the emitter happens to emit at a different wavelength, the antenna would have to be designed so that the maximum of C s (α) happens at that wavelength. This has been quantified in the Appendix B, where it is shown that the chirality can be boosted for wavelengths ranging from the UV to the IR.

Last but not least, the differences in behavior between the gold and silicon antennas are summarized in Fig. 7. We have carried out the simulations for a chiral emitter with |α| 2 = 0.9, at a 10nm distance from the surface of the antenna along the z axis, oriented along the z axis, and emitting at λ = 808nm. Their spectral behavior is shown at the bottom of Fig. 7, where the vertical magenta line indicates the wavelength of the emission at 808nm. Then, at the top, we compute |E s | 2 on a XY plane at 600nm from the center of the resonator. It is observed, that while the Si antenna scatters all light in the +1 helicity component, the gold nano-antenna scatters almost evenly between the two helicity components. As for the scattered power, at this particular wavelength, it is seen that the two helicity components add up to a similar amount. The resonator is made of gold. The light is scattered almost equally in both helicity components. c) Spectral plots of C s (α) and Q s for both resonators. The initial chirality of the emitter is also plotted as a black horizontal line. At 808nm (magenta vertical line), the Si resonator has C s Si (α) ≈ 1 boosting the initial chirality of the emitter, whereas C s Au (α) ≈ 0 yielding an almost achiral scattered field.

in the helicity basis [30-32, 45, 46]. Here, we will solve the Mie problem in the helicity basis to study the chirality of the field scattered by the spherical antenna.

The multipolar fields in the parity basis are well-known in optics [START_REF] Rose | Elementary Theory of Angular Momentum[END_REF][START_REF] Tung | Group Theory in Physics[END_REF][START_REF] Jackson | Classical Electrodynamics : Third Edition[END_REF]. We denote them as

A (e) jmz , A (m) jmz .
In contrast, the multipolar fields in the helicity basis are not very frequently used. They are linear combinations of electric and magnetic multipoles [30,46]:

A + jmz = A (m) jmz + iA (e) jmz √ 2 A - jmz = A (m) jmz -iA (e) jmz √ 2 (A.1)
As a result, A + jmz and A - jmz are eigenstates of the helicity operator Λ:

ΛA + jmz = +A + jmz ΛA - jmz = -A - jmz (A.2)
Notice that for both families of multipoles, the sub-indexes j, m z stand for the eigenvalues of the operators (J 2 ) and (J z ) [32]. Now, in order to solve the Mie problem (either in the parity or helicity basis), the decomposition of the incident field as a sum of multipoles needs to be found [START_REF] Gouesbet | Generalized Lorenz-Mie Theories[END_REF]. This will be the objective of the next section for the field emitted by the chiral emitter C.

The incident field

Let us consider the field emitted by the chiral emitter C at a given wavelength λ 0 . We will express the field with respect to a system of coordinates located on the emitter. Then, in the same way that the electric field emitted by an electric dipole p is given by an electric multipole of order j = 1, the electric field produced by p + is also given by a multipole of order j = 1 whose helicity content is +1. Now, it has been assumed that the emitter does not emit as a pure dipole p + , but rather as p + with a probability of |α| 2 and as p - with a probability of (1 -|α| 2 ). Hence, the electric field created by C will be:

E C (r) = αA + 1,mz + 1 -|α| 2 A - 1,mz (A.3)
In general, eq.(A.3) could be a summation over different values of m z , depending on the orientation of the dipoles of the emitter. Here, to make calculations simpler, we will suppose that m z has a fixed value m * z , which has to be either -1, 0, +1. Also notice that, due to their emitting behavior, the radial dependence of the multipolar fields in Eq.(A.3) are given by a spherical Hankel function h 1 (2πr/λ 0 ).

As mentioned earlier, E C is the electric field created by C expressed with respect to the frame of reference located at the center of the emitter. However, to solve the Mie problem, we need to express this field with respect to a frame of reference located at the center of the antenna. Let r 0 be the position of the emitter with respect to the center of the sphere. Then, the expression of E C (rr 0 ) in terms of multipoles can be found by using the so-called translation-addition formulas [55, p.171][58, App.C] [START_REF] Wittmann | Antennas and Propagation[END_REF]. Here, we will make two assumptions. First, without losing any generality, we will consider that the emitter is located along the z axis, i.e. the position of the antenna r 0 = r 0 ẑ. Second, we will consider that the emitter is located outside of the spherical antenna in consideration. Then, E C (rr 0 ) is expressed as:

E C (r -r 0 ẑ) =                  ∞ j =1 ∞ L=0 α T j ,L,1,m * z Rg A + j ,m * z + 1 -|α| 2 T j ,L,-1,m * z Rg A - j ,m * z if |r| < r 0 , ∞ j =1 ∞ L=0 α Rg T j ,L,1,m * z A + j ,m * z + 1 -|α| 2 Rg T j ,L,-1,m * z A - j ,m * z if |r| > r 0 . (A.4)
where T j ,L,p,mz is defined as:

T j ,L,p,mz = (2L + 1)(-i) L h L 2πr 0 λ 0 m z , 0(j , L)1, m z 1, p(j , L)p, 0 (A.5)

with J, M (j, j )m, m being the Clebsch-Gordan coefficients [START_REF] Tung | Group Theory in Physics[END_REF]. Note that it is assumed that both T j ,L,p,mz and A ± jmz have a radial dependence that is given by a Hankel function. Then, when a Bessel function dependence is needed, this is made explicit by the Rg {•} sign, e.g. in eq.(A.4).

The Mie problem

Due to the symmetries of the Mie problem, once the multipolar decomposition of the incident field is known, the field scattered by the antenna immediately follows. Now, for this case, the incident field is E C (rr 0 ẑ). However, E C (rr 0 ẑ) has a different multipolar decomposition if |r| ≶ r 0 . Here, we will use the expression of E C (rr 0 ẑ) for |r| = R, with R being the radius of the spherical antenna. As mentioned above, it will be assumed that the emitter is located outside the sphere, i.e. r 0 > R. Then, the incident field used to solve the Mie problem will be:

E i (α) = ∞ j =1 ∞ L=0 α T j ,L,1,m * z Rg A + j ,m * z + 1 -|α| 2 T j ,L,-1,m * z Rg A - j ,m * z (A.6)
As it was shown in [30,32], if the multipolar decomposition of the incident field is E i = j,mz α p jmz A p jmz , then the scattered and field inside of the sphere are given by:

E s = j,mz α p jmz a j + b j √ 2 A p jmz + a j -b j √ 2 A -p jmz E int = j,mz α p jmz d j + c j √ 2 A p jmz + d j -c j √ 2 A -p jmz (A.7)
where {a j , b j , c j , d j } are the so-called Mie coefficients [START_REF] Bohren | Absorption and scattering of light by small particles[END_REF]. Thus, using eqs.(A.6-A.7), we obtain that the emitter-antenna interaction results in the following scattered field:

E s (α) = ∞ j =1 ∞ L=0 α T j ,L,1,m * z a j + b j √ 2 + 1 -|α| 2 T j ,L,-1,m * z a j -b j √ 2 A + j ,m * z + α T j ,L,1,m * z a j -b j √ 2 + 1 -|α| 2 T j ,L,-1,m * z a j + b j √ 2 A - j ,m * z (A.8)
Eq.(A.8) models the effect that the antenna has on the light emitted by C. In order to quantify the effects of the antenna on a chirality measurement, we look at the ratio of the two helicity component of the scattered power. Due to the orthogonality between the modes of helicity + and -, we can separate the total scattered power W s as the addition of two terms with a well-defined helicity, i.e. W s = W s + + W s -. Each of these terms is computed as:

W s + = j ,L |α T j ,L,1,m * z a j + b j √ 2 + 1 -|α| 2 T j ,L,-1,m * z a j -b j √ 2 | 2 (A.9) W s -= j ,L |α T j ,L,1,m * z a j -b j √ 2 + 1 -|α| 2 T j ,L,-1,m * z a j + b j √ 2 | 2 (A.10)
Both W s and W s ± are given in power units. Then, in order to give dimensionless results for the scattering, scattering efficiency factors Q s have been computed throughout the manuscript. These are computed as the flux of the Poynting vector across a spherical surface, divided over the size parameter: Finally, in the same way as we did for the emitter in Eq.( 3), we can define the induced chirality of the antenna as:

Q s = Q s + + Q s -= W s λ 2 4π 2 R 2 = (W s + + W s -)λ 2 4π 2 R 2 (A.11) λ (
C s (α) = j ,L |α T j ,L,1,mz a j + b j √ 2 + 1 -|α| 2 T j ,L,-1,mz a j -b j √ 2 | 2 -|α T j ,L,1,mz a j -b j √ 2 + 1 -|α| 2 T j ,L,-1,mz a j + b j √ 2 | 2 j ,L |α T j ,L,1,mz a j + b j √ 2 + 1 -|α| 2 T j ,L,-1,mz a j -b j √ 2 | 2 + |α T j ,L,1,mz a j -b j √ 2 + 1 -|α| 2 T j ,L,-1,mz a j + b j √ 2 | 2
(A.12)

Eq.(A.12) is the main analytic result of this paper. Given the chirality of the emitter C(α), C s (α) predicts the induced chirality by the spherical antenna. Note that C s (α) is a multi-variable function. Not only does it depend on α, but it is also a function of other properties of the emitter such as λ 0 , m * z , r 0 . In addition, C s (α) depends on some parameters of the antenna, , µ, R.

APPENDIX B

In this section, we show that even though the study above has been done with small resonators, larger antennas do not improve the chirality features shown in Fig. 3. Using eq.( 5), we can compute the chirality of the scattering arbitrarily modifying the radius R of the antenna and the λ of the emission. The results are displayed in Fig. 8 for R = 30 -300nm, λ = 400 -1500nm, and |α| 2 = 0.9. Fig. 8 demonstrates that small antennas achieve a larger range of chirality values in the visible domain. For telecommunication wavelengths, similar chirality modulations are achieved, but the features of the antenna are spectrally widened. Now, as it is numerically shown next, the largest chirality modulations are consistently given in the intervals R = 50 -100nm and 450 -600nm. Actually, this fact is shown to be independent of the initial chirality of the emitter, modeled by α, even though α plays a quantitative role. To demonstrate this, in Fig. 9, we depict C s (α, R, λ) for |α| 2 = 0.6, 0.7, 0.8, 0.9 and R = 30 -300nm and λ = 400 -900nm. The antenna is made of Si. It can be seen that the shape of all the (R, λ) plots resemble each other. In contrast, the accessible values for C s (α), given by the colorbar, vary from one plot to the other. Actually, it is seen that the greater α is, the larger interval of chirality values the antenna can achieve.

Moreover, it is observed that most of the interesting phenomena occur for R ∈ [50 -100]nm and λ ∈ [450 -600]nm. These phenomena encompass inversion and boost of the initial chirality of the emitter, as well as dual and achiral behaviors. Thus, in Figure 10 we show C s (α, R, λ) for 4 different |α| 2 = 0.6, 0.7, 0.8, 0.9 and R = 50 -100nm and λ = 450 -600nm. Judging by the colorbars, it is seen that all the accessible chirality states are encompassed in this range.

FIG. 1 .

 1 FIG. 1. |E C | 2 of an emitting dipolar emitter. For a) and b) the dipole is oriented along the z axis, whereas for c) and d) it is left circularly oriented, i.e. p± ∝ (x + iŷ). The dipole emits light with helicity +1 in a) and c), and with helicity -1 in b) and d). The emission is at λ = 632nm. A null field has been assumed in a spherical volume of radius 100nm to remove the divergence of dipolar fields at the origin. Each image is 1µm×1µm in size.

  FIG. 2. a) Scattered far-field chirality signal. The black straight line represents C(α = √ 0.9), whereas the colored lines display C s (α = √ 0.9, R) for R = 40, 60, 80, 100nm. b) Scattering efficiencies (Q s ) for the same 4 antennas. c) Scattering efficiency factor (Q s + ) corresponding to a helicity +1 state. d) Scattering efficiency factor (Q s -) corresponding to a helicity -1 state. The same color code is used for all plots. All the multipolar contributions of the antenna are taken into account for all calculations. The antenna is made of Au.

FIG. 3 .

 3 FIG.3. In blue, plots of the scattered far-field chirality C s (α = √ 0.9, R). In black, the initial chirality of the emitter C(α = √ 0.9). In red, the scattering efficiency factor Q s . Each subplot a)b)c)d) corresponds to a different size of the resonator given by R = 40, 60, 80, 100nm. The resonator is made of Si. All the multipolar contributions have been taken into account for all the plots. The electric/magnetic dipolar and quadrupolar contributions have been explicitly marked. The chiral emitter has |α| 2 = 0.9, it is at a 10nm distance from the surface of the antenna along the z axis, oriented along the z axis, i.e. mz = 0. The permittivity of Si has been obtained from[52].

FIG. 4 .

 4 FIG. 4. A chiral dipolar emitter with |α| 2 = 0.9 in the λ = 400 -900nm range interacts with an antenna of radius R = 100nm made of Si. a) C s (α = √ 0.9) in red and C(α = √ 0.9) in black. b) Scattering efficiency factor Q s for the antenna. c) Helicity +1 component of Q s (Q s + ) in red, and the probability of the emitter to emit in a helicity +1 state (|α| 2 = 0.9) in black. d) Helicity -1 component of Q s (Q s -) in red, and the probability of the emitter to emit in a helicity -1 state (1 -|α| 2 = 0.1) in black.

FIG. 5 .

 5 FIG. 5. Comparison between the chirality emitted by a Si-based resonator and its duality behavior. a) C s ( √ 0.9, R, λ) in red and the initial C( √ 0.9) in black. b) log 10 T (R, , µ) -1 . Both plots have been done with a Si-made antenna of R = 100nm. All multipolar contributions are taken into account.

FIG. 6 .

 6 FIG.6. Chirality dependence on the size of the antenna. The black horizontal line represents the initial chirality of the molecule C(α = √ 0.9) = 0.8. In red, the scattered chirality C s (α = √ 0.9, R = 100). The vertical magenta line highlights the wavelength at which C s reaches a maximum. The green and blue lines are obtained using particles with R = 98, 102nm respectively.

R

  = 100nm. Light is emitted at λ = 808nm and the emitter is oriented along the z axis. The scattered field is measured at a XY plane at 600nm of the center of the resonator. The scattered field is projected into its two helicity components. a) The resonator is made of silicon. Most of the light is scattered in the +1 helicity component. b)

8 FIG. 8 .

 88 FIG. 8. C s (α = √ 0.9, R, λ) for R = 30 -300nm and λ = 400 -900nm. The antenna is made of Si.

FIG. 9 .

 9 FIG. 9. Influence of the initial chirality of the emitter on the chirality of the scattered field by the antenna. C s (α, R, λ) for R = 30 -300nm and λ = 400 -900nm is plotted for a) α = √ 0.6, b) α = √ 0.7, c) α = √ 0.8, α = √ 0.9. The antenna is made of Si.

FIG. 10 . 9 .

 109 FIG. 10. Influence of the initial chirality of the emitter on the chirality of the scattered field by the antenna. C s (α, R, λ) for R = 50 -100nm and λ = 450 -600nm is plotted for a) α = √ 0.6, b) α = √ 0.7, c) α = √ 0.8, α = √ 0.9. The antenna is made of Si.

ACKNOWLEDGMENTS This work has been carried out thanks to the support of the A*MIDEX project (n • ANR-11-IDEX-0001-02) funded by the Investissements d'Avenir French Government program managed by the French National Research Agency (ANR).

We have presented a formulation based on the multipolar theory developed in the helicity basis to quantify the chirality of the field emitted by a system composed of a chiral dipole coupled to an optical antenna. First, it has been seen that gold spherical antennas do not feature the ability to tailor the chirality of emitted fields since they yield the same achiral response in the whole visible/near infrared range. This is due to the fact that plasmonic spherical nanoparticles behave mainly as electric dipoles. A very different feature was observed with silicon-made spherical nanoantennas. It has been shown that they are highly efficient to manipulate chiral fields emitted by dipolar emitters. They can yield scattered fields which almost encompass all the possible values of chirality, from C s = -1 to C s = +1 (see Fig. 7). Given an emitter with an intrinsic chirality, the antenna can boost or reduce the chirality in the far field region. In particular, the antenna can yield a field with the exact same chirality of the emitter at the dual condition, and it can also yield completely achiral fields at the electric/magnetic resonant conditions. This result shows that transparent mono-disperse colloidal solutions of silicon particles could potentially be used to produce strong chiral effects with emitters.

Appendix A

In this section, we lay out the analytic formalism that will be used to compute the light-matter interaction between a single chiral emitter and a spherical resonator. Due to the symmetries of the problem, we will solve the problem using Mie theory. Mie theory is usually expressed in the electric/magnetic (or parity) basis. Nonetheless, in order to deal with chirality problems, it is more convenient to re-express the problem


Jean-Luc Vinot
email: jean-luc.vinot@enac.fr

Sylvie Athènes

Legible, are you sure? An Experimentation-based Typographical Design in Safety-Critical Context

Keywords: Design, evaluation, experimentation, typography, legibility, readability, Safety-critical, aircraft, cockpit. ACM Classification H.5.m. Information interfaces and presentation (e.g., HCI): Miscellaneous Design, Experimentation, Human Factors

Designing Safety-critical interfaces entails proving the safety and operational usability of each component. Largely taken for granted in everyday interface design, the typographical component, through its legibility and aesthetics, weighs heavily on the ubiquitous reading task at the heart of most visualizations and interactions. In this paper, we present a research project whose goal is the creation of a new typeface to display textual information on future aircraft interfaces. After an initial task analysis leading to the definition of specific needs, requirements and design principles, the design constantly evolves from an iterative cycle of design and experimentation. We present three experiments (laboratory and cockpit) used mainly to validate initial choices and fine-tune font properties. Results confirm the importance of rigorously testing the typographical component as a part of text output evaluation in interactive systems.

INTRODUCTION

When designing safety-critical interactive system, one needs to evaluate them against the requirements of Safety, Usability, Reliability and capacity to Evolve (SURE) [START_REF] Palanque | usability for safety critical systems: how to be sure (safe, usable, reliable, and evolvable)[END_REF] that can be seen as convergent and always desirable properties. Evolution in the design of safety-critical HMI calls for a change in the way we conceive of the links between user needs, system constraints, requirements and validation.

As part of a research cooperation with aeronautical industry, we were asked to go over text information visualization for all screens (cockpit and cabin) of future aircraft programs. The goal was to create a set of specially adapted fonts. Additionally, we had to establish the rules of use for these fonts geared to future cockpit interfaces, in order to provide design engineers with relevant information about the relationship between font specificities and context of use.

Cockpit screens, as others Safety-critical interfaces, are essentially based on the display of textual information and, thus, rest on the use of digital fonts. The large number of available digital fonts, as well as the published guidelines should not lead us to consider that legibility is no longer an issue of concern. On the contrary, a special effort should be made to prove the safety, usability and performance of this software component. The creation of a numeric typeface necessarily involves highly specialized knowledge in the field of design and typography. The critical area of use of these fonts also requires the contribution of particularly rigorous evaluation methodologies of the kind used by experimental sciences. In aeronautical context, design, development and operational deployment are strictly supervised by system engineering methodologies, evaluation and finally, technical and users' validation required for certification and approval of new operational systems.

This paper presents a study involving the design of typeface suited for cockpit, its development and evaluation. We present the different phases making up the study: task analysis, description of the specific needs, links with theoretical work, definition of the ensuing requirements and design principles and, lastly, an iterative process of designexperiment cycles geared to help and validate design choices. Among tests designed at the character, word or whole page levels, only results from three detailed experiments pertaining to character discrimination are reported here as a coherent whole within our design process. Finally, we conclude with a discussion of the contributions of this kind of integrated study within the design process and the possible implications for HCI.

PRELIMINARY ANALYSIS

This project required significant preliminary analysis: a phase of field observations of users in an operational context with pilots (simulator and real commercial flights), an expert analysis of the existing technical constraints, and a theoretical approach based on established knowledge from two domains, the perceptual processing of visual information and the typography.

Analysis of pilots activity

On commercial flights, pilot crews ensure five major activities: aircraft piloting (manually or with autopilot), navigation (managing and tracking flight route plan), aircraft systems monitoring, communication with air-traffic controllers and ground support, and lastly, management of the airline mission. In order to conduct these activities, they interact with specialized interfaces displayed on the cockpit screens. The increasing complexity of aircraft systems leads today to a more integrative approach with an aggregation of cockpit systems, and a significant increase in data and functions displayed for pilots. These complex visualizations may cause new risks to the usability of systems.

Observations of pilots in the cockpit have shown that both display environment and data have very special characteristics, thus entailing highly idiosyncratic needs. Below are listed the most important ones.

[N1] Extreme lighting conditions: pilots ceaselessly look from one screen to another in order to gather and compile information. Additionally, the visual transition between the aircraft inside and outside can be very abrupt. These constant adaptations to brightness and focus generate visual discomfort and fatigue.

[N2] Viewing angles: Multi-screen display in the cockpit implies that pilots have to read data viewed from different angles and distances.

[N3] Time pressure: Visual fixation dwells, which require more time for denser and more complex information [START_REF] Bellenkes | Visual scanning and pilot expertise: The role of attentional flexibility and mental model development[END_REF], will however be shortened in heavy workload context [START_REF] Wickens | Engineering Psychology and Human Performance[END_REF].

[N4] Specific data: Texts are very specific: mostly symbolic and non-textual information, numerical values, system IDs, aeronautical abbreviations, labels or abbreviated sentences for menu or instruction lines, and even mixture of letters and numbers.

[N5] Text legibility: Text density can be quite overwhelming. Character design itself has some flaws that tend to bring about confusion between some letters. Significant problems were found concerning visual spacing, letter size or contrast. Lastly, fonts used on different views are sometimes heterogeneous. The close proximity or overlapping of graphical elements (highlights, framing, weather information, maps) can significantly interfere with legibility.

Results from this analysis allowed us to define a multidisciplinary process to design, guided by theory and validated progressively through experimental studies. We first researched relevant models from theoretical work in order to translate the previously defined needs into design requirements.

Related theoretical work

For anyone whose work implies presenting textual information, whether printed on paper or displayed on screen, there is a large corpus of knowledge and rules meant to facilitate text legibility, ranging from font size, colour and contrast choices, to spacing and text disposition. While making good use of this literature, the specific operational environment -aircraft safety-critical interfaces -drove us to explore more fundamental aspects of the reading mechanisms and use typographical knowledge and approach. On the one hand, time pressure, fatigue, extreme lighting contexts and heterogeneous complex data are seriously constraining text display. On the other hand, there is a much larger than usual expectation from the reader about the kind and whereabouts of the displayed information. Opening our study to new solutions meant fitting our specific reading context within the available knowledge about basic reading mechanisms.

During reading, the eyes move across the text, mingling short rapid movements and, about four to five times per second, short stops. This succession of saccades and fixations allows for groups of characters to be successively projected onto the central part of the retina, where they enter the nervous system to be further processed. This part of the retina, the fovea, is extremely small -1 or 2 degrees of visual angle-and is responsible for the most precise visual perception. In normal reading conditions, this area perceives at the same time 4 to 5 characters with great precision. Swift movements across the text, the saccades, tend to jump over 7/8 characters -the range being 1 to 20 characters -and serve to bring the fovea to the next relevant group of characters for a fixation. Saccade lengths, fixation durations and regressions to text already read vary considerably with reader experience and text difficulty.

The retina is not homogeneous, leading to considerable differences in the perceptual capacity of the central versus peripheral parts of the receptor field. We perceive precisely only the small part of the visual field which is projected on the fovea. Starting from this area, the rest of the visual field becomes progressively blurred [START_REF] Sere | Nonhomogeneous resolution of images of natural scenes[END_REF] [START_REF] Nazir | On words and their letters[END_REF]. Nevertheless, as far as reading is concerned, character size is not a decisive factor for the reading performance: smaller characters are not more difficult to read than bigger characters. Indeed, increasing the character size increases by the same token the peripheral area covered by any given number of characters, causing those falling outside of the fovea to become blurred. In contrast, smaller characters allow the eyes to perceive precisely a larger number of letters. Within limits of the retina resolution, the two mechanisms, central precision and blurred periphery, compensate each other, so that small and large characters tend to yield equivalent reading performances.

Saccade lengths tend to be rather constant in number of characters whereas they vary greatly in size, depending on the text font. Based on the number of characters -typically 7 to 9 -the brain anticipates the amount of eye movement necessary for the saccade to jump over the right number of characters, regardless of their size. Seven to 9 seems therefore to be the amount of characters processed during a fixation. Processing time can be extremely brief. Although the average fixation duration is about 200ms, a display duration of about 50ms allows for reading to proceed normally [START_REF] Mcconkie | The span of the effective stimulus during a fixation in reading[END_REF]. While the fovea identifies exactly the characters, the peripheral vision uses their global shape in order to anticipate the words yet to be processed [START_REF] Nazir | Letter visibility and word recognition:The optimal viewing position in printed words[END_REF]. Obviously, some characters are easier for the peripheral vision to discriminate, for example, "i" and "p", or "l" and "m". Studies have proposed to cluster letters according to specific parts of their anatomy (stem, ascender, descender…) [START_REF] Jacobs | Perception of lower letters in peripheral vision: A discrimination matrix based on saccade latencies[END_REF]. Most probably, when character shapes are very close (for example, "a" and "e"), the brain additionally uses linguistic regularities and semantic context to help anticipation. In fact, Reicher [START_REF] Reicher | Perceptual recognition as a function of meaningfulness of stimulus material[END_REF] showed a Word Superiority Effect where letters embedded within words are identified faster than when they are presented in isolation. More recent work by Pelli et al. [START_REF] Pelli | The remarkable inefficiency of word recognition[END_REF] nuances this effect by showing that a word is never detected as a single feature but more likely as a set of simple features detected at the letter level. Such results support the idea that reading involves detection and likelihood of features at several levels at the same time, characters, graphemes, syllables and words, each level providing a linguistic context to help recognition. However, any Word Superiority Effect is of limited use for deciphering some of the specific data displayed in aeronautical context where legibility may rest crucially on the discrimination between individual characters in order to disambiguate non words.

Visual perception and spatial frequencies

Visual perception can be described in terms of spatial frequencies or, in other words, as a number of cycles per degree of visual angle. One can very simply visualize this notion as a grid of very thin black vertical lines on a light background: our perception is best when there are 8 lines (or cycles) per degree of visual angle. Above 50-60 cycles per degree of visual angle, most people perceive only a uniform grey. While being a good approximation of a standard situation, these results are not absolute and depend on display contrast. Any letter of a given size at a given distance from the eyes can be described in terms of spatial frequencies: the global shape will be defined by lower frequencies whereas fine details will come from higher frequencies.

Enhancing legibility

We already stated that the specific organization of the retina entails a decrease in visual precision from the fovea to the periphery. Another way to describe this phenomenon is to express this decrease in terms of a differing sensitivity to spatial frequencies: the fovea is sensitive to high frequencies whereas the periphery is sensitive to low frequencies. Spatial frequency is thus a very useful notion to describe and compare character shapes [START_REF] Rubinstein | Digital Typography: an Introduction to Type and Composition for Computer System Design[END_REF]. Basic character strokes are vertical, horizontal or diagonal, straight or curved. In a normal comfortable reading situation, the frequencies making up the character basic strokes are low, typically 6 to 8 cycles per degree of visual angle, while details, such as serifs, are high frequency components [START_REF] Rubinstein | Digital Typography: an Introduction to Type and Composition for Computer System Design[END_REF]. More recently, Majaj et al. [START_REF] Majaj | The role of spatial frequency channels in letter identification[END_REF] proposed the concept of stroke frequency, i.e. the number of lines crossed by a slice through a letter, divided by the letter width. As a result, global -lower frequency-shape of the characters will be well perceived by the peripheral retina, but details will be perceived only by the central retina (aka fovea). In order to help character discrimination by the peripheral retina, and therefore facilitate word anticipation and presumably reading, one has to pay attention to the low frequency components of the characters.

Enhancing readability

Highly readable displays allow for good anticipation and less demand on attention [START_REF] Wickens | Engineering Psychology and Human Performance[END_REF]. When the characters projected on the peripheral retina are too blurred to be read, the brain still uses the perception to detect alternating space and characters, and word length. In order to enhance further readability, one should pay attention to the relationship between the inner spaces of the character, the spacing between characters and between words.

Typographical means

The field of Typography produced a large corpus of knowledge and rules, commonly used by designers to address typographical needs of interfaces. Today, management and rendering technologies for digital text are very efficient. The available type library (digital fonts) for many languages and uses is large, but primarily intended for displaying text written as sentences. For our own needs, the display of specific textual information in Safety-critical context, we had to go back to the foundations of typography, letter anatomy, composition and harmony. We conducted a detailed anatomical study of alphanumeric characters. We described the structural elements of stroke and listed the main characteristics to be safeguarded for each glyph.

Letter Anatomy and typographic contrast

A font is a typographical representation of writing, consisting of a set of characters. In digital font, characters are instantiated by glyphs, images (graphemes) of typographical sign [START_REF] Haralambous | [END_REF]. The shape of these typographical signs is built from regular stroke parts corresponding to basic gestures of the character writing. Five standard parts describe the academic drawing of most Latin letters anatomy: the stem, e.g. the vertical line of I character, the arm or crossbar, e.g. the horizontal lines of E or A, the stroke, e.g. the diagonal branches of A or K, the bowl, stress or spine, e.g. the curved strokes of O or S, the leg or tail of R or Q. Along with these five parts, there are many other anatomical elements such as spikes (A) or loop (g), ascenders and descenders (projecting parts of lowercase letters), or serifs (small endings, originally induced by the tool used for drawing a letter).

Typographic contrast is the variation in thickness between the thicker and thinner parts of the character. Some lineals (sans serif) typefaces, such as Arial, have a very low contrast, thus inducing simpler, more basic shapes, than Oldstyle type, like the Times New roman used for this text. Typographic contrast is used to reproduce writing gestures and is thus better suited to visually express the stroke parts making up a character.

Harmony, visual alignments and spacing

For typography, harmony is based on balance and visual consistency of form and composition. Character drawing is based on three main visual horizontal alignments: baseline, cap-height and x-height (lowercase). Traditionally, stroke and contrast regularities are produced by the writing implement, oriented to form a slanted axis for character drawing. For Typographers, spacing is one of the most important issues to address. The visual balance of inner spaces of each character shape (counter-forms) and the regular spacing between letters and words are fundamental. Due to the constraints of pixels at low resolution, counter spaces are especially difficult to adjust in digital fonts.

Respect for the letter anatomy and visual alignments, good use of typographic contrast and balanced spacing are essential to the legibility and harmony of typefaces [START_REF] Larson | Measuring the aesthetics of reading. People & Computers XX -ENGAGE[END_REF].

Typographical invariants: the font properties

Digital fonts are categorized by properties, such as weight (regular, bold) or slant (roman, italic) called typographical invariants. A typeface includes a set of fonts that express these properties. Creation of fonts requires fine-tuning of these properties.

Legibility of digital fonts

Adrian Frutiger [START_REF] Frutiger | Homme et ses signes[END_REF] worked for the signage system of Roissy-Charles de Gaulle Airport in France. He designed the typeface to ensure maximum text legibility, both from afar and from various angles. Among others, he tested the visual robustness of blurred characters. The high quality of Roissy typeface is due both to extensive work on the design of letter (large aperture, subtle optical corrections) and to a carefully balanced and aesthetical typography. This work led to the creation of the Frutiger typeface which was used for roadway signage in France and Switzerland and many transit systems around the world.

Microsoft's Verdana typeface [11], was designed by Matthew Carter and hinted by Tom Rickner specifically to address good readability of text on screen and rendering of scalable characters, even for low resolution devices. In these fonts, incorporating many hand-hinting instructions enhances pixel rasterization. They attempt to correct undesirable rasterization effects of glyph by equalizing the weights of stems, arms or stroke letter anatomy, thus preventing parts of glyphs from disappearing. As a consequence, even for low resolution, hinting maintains legibility and aesthetic appearance. More than the important work on shape and discrimination of characters, one of the unique qualities of Verdana is the regularity of the spacing (inside and between letters), producing an excellent readability.

French Air Navigation Services have conducted studies on the specific typographical needs for air traffic control interfaces in safety-critical context. Similarly to cockpit screens, the data displayed on the controller's radar screen are very specific. Especially tricky are callsigns (aircraft ID), a mixture of letters and numbers where two callsigns may differ by only one character, for example, AF974ZL and AF9747L. Both bitmap (ODS) and vector (Bleriot) digital fonts families have been designed to enhance legibility and ensure discrimination between characters. These fonts have been evaluated and recommended in a Eurocontrol study [START_REF] Directed By Jackson | CoRe Project -Baseline Exemplary Style Guide[END_REF] and are currently used for ATC and aircraft systems.

FROM REQUIREMENTS TO DESIGN PRINCIPLES

Building on the needs defined in the activity analysis phase and the theoretical approach, we were able to list the requirements necessary to guide the design and, whenever possible, to highlight and scientifically express important issues. We then proceeded to design a first prototype of a cockpit suited typeface. These requirements relate to major aspects of typography traditionally defined by the terms of legibility and readability. In addition, we had to take into account more technical requirements to comply with current layout constraints of cockpit screens.

Requirements

[R1] Legibility concerns more specifically the form and the visual rendering of each individual character. Particularly in Safety-critical systems and for specific data, each glyph, even isolated, must be completely identifiable and easily discriminated from other glyphs. As already stated, glyphs should ideally be distinguished from one another solely on the basis of low-frequency visual information [START_REF] Rubinstein | Digital Typography: an Introduction to Type and Composition for Computer System Design[END_REF].

[R2] Reading performance must be maintained in spite of short visual fixation durations and be resistant to low degrees of visual angle and high angular distortions.

[R3] Robustness in degraded visual environment is necessary to address the risks of high external light changes leading to a significant loss of text contrast. In complex graphic context, it is also necessary to address multi-layout interfaces and text superposition with other graphical objects.

[R4] Readability results from the complete process of presenting textual material in order to communicate meaning. In typography, readability strives to improve reading efficiency through coherence and regularity of text disposition, and letter proportions and contrast.

[R5] Reading comfort concerns the regularity of shapes, visual alignments, spacing and composition of characters in text string [START_REF] Mcconkie | The span of the effective stimulus during a fixation in reading[END_REF], and should allow for better planning of visual saccades.

[R6] Compliance with the layout constraints of current cockpit display models refers to the capacity to maintain, for example, text sizes and characters per line density, strict vertical alignment for each character of a given displayed data, or specific charset.

[R7] Semantic soundness entails that the typeface, in a general sense, must be in harmony with the meaning of aeronautics.

Translating these requirements into typographic design principles is difficult because these set of requirements are partly conflicting or highly dependent. Thus, comfort of reading requires regular shapes whereas legibility in aeronautical context requires increasing visual distance between glyphs; or compliance with current text density on cockpit screen coerces character width and can interfere with the legibility or readability. Of all the requirements listed above, only R1 to R6 have been tested ; R7 has been taken into account in the design but not tested.

Design principles

We have identified a set of typographical recommendations for design, not strictly limited to, but including: Typeface will strictly express basic stroke parts of letter anatomy (in accordance with our anatomical study) to provide good character identification (R1, R2, R3). The shape of each alphanumeric letter will be particularly differentiated from the shape of other characters with which it could be confused Links and junctions between basic stroke parts of each letter will be carefully drawn to ensure clarity at low resolution and increase reading performance (R2). Numeric characters will use specific forms such as slashed "0", open form of "4" or a large hook for "1", to ensure that numbers will be perceived as a separate set and not be confused with capital letters (R3). Character width will be carefully reduced as condensed font form in order to ensure text density compliance (R6) while being visually robust to angular distortion (R2). Width of numeric characters will be strictly equalized to allow vertical alignment of numeric values (R6). Typographical contrast (thickness variation of character strokes) will be strong enough to guarantee symbol unity and robustness in complex graphic context (R3). X-height alignment of the font will be low enough to yield a good contrast of lowercase ascender and to improve text prediction in peripheral vision (R1, R2). Kerning will be specially adjusted to display short words and alphanumeric values in compliance with aeronautical needs (R4, R6). Fonts will use hinting instructions to ensure good display for low-medium resolutions (R2, R5, R6). Typeface will be both visually stern and aesthetic to satisfy pilots and be in harmony with the semantic of aeronautics (R5, R7).

FIRST DESIGN PHASE

We used the above listed requirements and design principles to conduct a first typographic design and produce a sofware prototype of the font.

Analysing readable fonts

We first performed a morphological comparison of sans serif fonts reputedly designed to maximize readability in order to analyze their forms and properties. Overlapping of glyphs shows a high overall similarity of forms, with some interesting variations for some signs, for example glyphs "Q" or "3" (details on Figure 1). Proximity of the main typographical invariants values (weight, character width) of these fonts allows us to consider them as reference values for our experimental exploration of font properties.

Regardless of their qualities, none of these fonts satisfies all the requirements. The most difficult requirement is compliance with cockpit layout constraints (R6).

Exploring solutions

Figure : visual comparison after applying a Gaussian blur on the glyphs "8" and "B" of three fonts.

One of our design principles is to discriminate glyphs on the basis of low visual frequencies and thus improve the prediction of the characters in peripheral vision. For a lowresolution text rendering, rasterization of characters adds blur to the glyphs (antialiasing) and smooth angles of visual forms. Figure 2 illustrates this visual effect by applying a Gaussian blur on a pair of characters (8, B), displayed using 3 different fonts: aeronautical, Verdana and Helvetica Neue.

Figure : half-bitting rendering technique (left); two modified glyphs blurred and not blurred (right)

Rubinstein [START_REF] Rubinstein | Digital Typography: an Introduction to Type and Composition for Computer System Design[END_REF] proposes the use of the Half-Bitting technique to improve the rendering of printed text (laser printer) with more subtle visual strokes. This technique allows, for example, to increase an angle by adding or removing pixels at opposed outgoing and incoming angles of the form (figure 3, left), in a fashion similar to the one used by artists to increase the salience of angles by extending or distorting the edges. The rendering visually enhances the characteristics of the expected form.

We have used special serif forms, like glyphic (incised) typefaces, to test the visual increase of angles and junctions of stroke parts. This form is compatible with the design of lineals sans serif fonts and can be achieved by the creation of light serifs, thickening the extremities of shapes like the Optima fonts. Figure 3 (right) shows two modifed glyphs of the first prototype (with and without Gaussian blur). Even after blurring, the glyphs remain visually well discriminated.

Designing the typeface

Taking into account the previous remarks and requirements, the next step was to instantiate a typeface. This typographic creation rests on a calligraphy work, calling for use of a drawing tool on paper. After a paper study with roughs, a reduce set of characters was drawn in large format, then scanned and vectorized. Bezier paths of letters were finalized and harmonized. Using these vector shapes, a first TrueType font (figure 4) was then created with the outline font editor FontForge, including uppercase and lowercase alphabets, numbers, and ASCII punctuation and symbols.

Figure : first font prototype (numbers and capitals letters)

ITERATIVE CYCLES OF DESIGN AND EVALUATION

Once this first prototype achieved, we developed a continuous interactive process of design and experimentation in order to explore potential typographic solutions, to verify the requirements and to progressively adjust the graphic properties of typeface.

Experiment 1

The goal of the first experiment was to position our prototype in terms of legibility and character discrimination. We thus compared a font widely used in aeronautical context, a font well-known for its good readability (Verdana) and our first font prototype. In order to enhance the role played by lowfrequency components in character recognition, the stimuli were displayed with a low character/background contrast which was adapted for each subject with the help of a pre-test.

Twelve subjects (aged 21 to 47) named characters (letters and numbers) which were briefly presented on a screen (LCD 30" Apple Cinema HD display) set either 80cm or 100cm away from the subject. A device bolted to the table maintained the subject/screen distance.

Pre-test

Each session started with the above-mentioned pre-test: seated 100cm away from the screen, the subject was briefly presented with a Landolt C (a ring with a gap oriented in various positions) and had to report its orientation (top, bottom, left or right) using the arrows on the keyboard. The size of this symbol was 4.75mm, the same as the character size used in the experiment. Twenty contrast values were used for the test: starting with a good contrast, each following symbol was stepwise displayed in a decreasing contrast value. After the 20 decreasing steps, the process was reversed and, starting with the last, virtually unperceivable, contrast value, it was stepwise increased back to good contrast values. A sound was emitted when the symbol was displayed and if the subject could not perceive its orientation, s/he was to report it by depressing the space bar. Results were scanned and an appropriate contrast value was chosen in the response range between "always correct" and "never perceived". This contrast value was used throughout the subsequent experiment.

Experimental task and settings

The subject had to name as quickly as possible the character which was displayed on the screen center. "Not identified" was also a possible response. For each font (aeronautical, Verdana and the prototype), thirty-six characters (26 letters: A to Z; 10 numbers: 0 to 9) were presented. Figure 5 illustrates the three fonts. A trial started with the display of a fixation pattern on the screen center during 700ms, followed by the display of the character at the same location during 17ms, then followed by a 200ms-span without display, during which time the subject gave the response. The next trial started with the display of the fixation pattern. A block consisted of the successive display of the 36 characters for one given font. Within each block, the characters were pseudo-randomly presented. For each experimental condition, there were 2 blocks. The subject could rest at will at the end of any given block.

Independent variables

There were 2 independent variables: the 3 fonts (aeronautical, Verdana and prototype) and the 2 subject/screen distances (standard 80cm and more difficult 100cm). The font and distance variables were counterbalanced on the subjects.

Dependent variable

There was only one dependent variable: the subject's response which could be "correct", "wrong" or "no-response" (meaning that the subject could not identify the character).

Results

Results are presented on Figure 6. For each type of responses (correct, wrong and no-response), an ANOVA with a repeated measures within subject design (3 fonts x 2 distances) was performed. The ANOVAs showed significant effects of the distance: the larger distance (d2) entailed an increase of the number of no responses (F(1,11) = 27.16, p = 0.000), an increase of the number of wrong responses (F(1,11) = 62.14, p = 0.000) and a decrease of correct responses (F(1,11) = 125.37, p = 0.000). Sustained by significant pairwise comparison, the ANOVAs showed also an effect of the font: Verdana and the prototype font both produced less no responses than the aeronautical font (F(2,22) = 35.52, p = 0.000); the prototype font gave rise to more correct responses (F(2,22) = 104.79, p = 0.000) and less wrong responses (F(2,22) = 25.39, p = 0.000) than Verdana, which itself fared significantly better than the aeronautical font. Significant interactions showed that the effect of the distance was greater for the aeronautical font, decreasing the number of correct responses (F(2,22) = 4.3, p = 0.042) and increasing the number of no responses (F(2,22) = 24.44, p = 0.000). In contrast, for the prototype font and Verdana, the effect of the distance was larger on the number of wrong responses (F(2,22) = 4.24, p = 0.028). In other words, with increasing distance, the aeronautical font became illegible whereas the prototype font and Verdana gave rise to more errors. To sum up, the prototype font and Verdana produced, by and large, results which were fairly similar and significantly better than the aeronautical font. Though of a different magnitude, there was also a slight, but significant advantage for the prototype font over Verdana.

Confusion matrix

In order to better understand the role of features for letter recognition, we generated letter confusion matrices [START_REF] Bouma | Visual recognition of isolated lowercase letters[END_REF]. Such matrices show the relationship between the displayed stimulus and the response given. It is a somewhat indirect but useful measure of character shape similarity. Figure 7 shows detail of a matrix.

By and large, for the aeronautical font, the distribution of confusion between characters is quite spread out, many confusions being made only once; no-responses are numerous and correct responses range from 2 to 14. These results reflect the great difficulty in discriminating the glyphs, especially at the larger distance. In contrast, Verdana and the prototype font confusion matrices yield tighter distributions, reflecting mostly known confusions between characters. For prototype font, major confusions are: I for 1 (9 occurrences), S for 5 [START_REF] Jacobs | Perception of lower letters in peripheral vision: A discrimination matrix based on saccade latencies[END_REF], Z for 7 (6) or Z for 2 (4), N for H [START_REF] Directed By Jackson | CoRe Project -Baseline Exemplary Style Guide[END_REF]. The correct responses are displayed on the diagonal of the matrix (stimulus "A" and response "A"...). All other cases are wrong answers, e.g. stimulus "5" and response "S". The far right column (on blue) presents the number of no-responses for each character.

Experimentation 2

The goal of this second experiment was to repeat our first experiment within the context of a cockpit, using the displays, orientations and distances from the screens as they are in aircrafts. We thus compared the same 3 fonts as in experiment 1 (a font widely used in aeronautical context, Verdana and our prototype), using the same experimental design. In the following section, the experimental information will be reported in detail only when departing from experiment 1.

Twelve subjects (aged 25 to 35) named characters (letters and numbers), which were briefly presented on a screen. As in the first experiment, the stimuli were displayed with a low character/background contrast, which was adapted for each subject with the help of a pre-test.

Experimental task and settings

The only departure from the settings of experiment 1 was the length of time during which the characters were displayed on the screen. Due to technical constraints, in order to ensure display of the character on cockpit screens, it had to be displayed over 2 cycles, thus during 34ms (as opposed to 17ms for experiment 1). Independent variables and dependent were the same as in experiment 1.

Results

Results are presented on Figure 8. For the "correct" and "wrong" type of responses, an ANOVA with a repeated measures within subject design (3 fonts × 2 distances) was performed. The number of "no-response" was to low to allow for an ANOVA, so that when reasonable a chi2 was calculated. The ANOVAs showed significant effects of the distance: the larger distance entailed an increase of the number of wrong responses (F(1,11) = 51.34, p = 0.000) and a decrease of correct responses (F(1,11) = 129.26, p = 0.000). The ANOVAs showed also an effect of the font: the prototype font gave rise to more correct responses (F(2,22) = 64.04, p = 0.000) than both Verdana and the aeronautical font (post hoc pairwise comparisons show significant effects, p = 0.000) and less wrong responses (F(2,22) = 30.19, p = 0.000) than Verdana, which itself fared significantly better than the aeronautical font. Results from the chi2 on the "no-responses" showed a significant effect of the font (Chi2(2) = 24.62, p < 0.000). Significant interactions showed that the effect of the distance was greater for the aeronautical font, greatly decreasing the number of correct responses (F(2,22) = 11.52, p = 0.000) and increasing the number of wrong responses (F(2,22) = 3.59, p = 0.045), as well as the number of no-responses (Chi2(5) = 185.47, p < 0.000).

Comparison between experiments 1 and 2:

We found the same trends in both experiments where the aeronautical font scores notably worse than both Verdana and the prototype. The main difference between the two experiments lies in the overall level of performance. Due most probably to the longer display time (34ms instead of 17ms), results from the cockpit simulation show a larger amount of correct responses and a smaller amount of wrong or no-responses. It is interesting to note that, whereas the decrease of no-responses in the cockpit setting is of the same magnitude for all 3 fonts (78% on average), the increase of correct responses, as well as the decrease of wrong responses set the aeronautical font apart. Indeed, the increase of correct responses is on average greater for this font (45% versus 14% and 17% for the prototype and Verdana respectively). The increase reaches 67% for the aeronautical font at the larger distance, versus 23% and 26% for the prototype and Verdana respectively.

Concerning the decrease of wrong responses, it is on average the same for all 3 fonts (about 28%). However, whereas the decrease is of the same magnitude for the prototype and Verdana irrespective of the distance (between 26% and 31%), it varies from 48% at the smaller distance to 5% at the larger distance for the aeronautical font. In other words, the longer display time of the stimuli in the cockpit helped all fonts, but it did so to a greater extent for the aeronautical font. Furthermore, for this last font, the larger distance still proved to be an hindrance that the longer display time did not compensate. Noteworthy is the fact that the rough prototype fares slightly but consistently better than Verdana.

Experimentation 3

The goal of this experiment was to help the design in setting a correct value for the character weight, taking into account that the characters would be displayed using different polarities (on black, white or gray backgrounds).

In order to evaluate the robustness of each tested weight, we used 2 character/background contrast values. In this experiment, we used only instances of the prototype font.

Twelve subjects (aged 21 to 57) performed a visual search task (letters and numbers). At the end of the session, using the pairwise comparison method, subjects were shown samples of the characters from the experiment and asked for their preferences.

Experimental task and settings:

The subject was presented with a 10 x 10 characters table displayed on a screen (LCD 30" Apple Cinema HD display) placed 80cm away and had to search for a given target character among distractor characters. Once the search was completed, the subject gave the number of occurrences he thought was correct. There was no limit to the search time, even though the instructions emphasized speed and accuracy. A trial started with the display of a round target pattern on the screen center during 500ms, followed by the display of the character to be searched during 1s. The 10 x 10 table was then presented centered on the screen. When the subject was finished, s/he depressed the space bar, which caused the table to disappear from the screen, and announced the number of occurrences s/he had found. For any given trial, the number of occurrences of the target character could pseudo-randomly be 1 to 5.

Taken from our prototype font, there were 36 distractor characters (numbers: 0 to 9; letters: A to Z) and 18 target characters, numbers and uppercase letters (0, 1, 2, 4, 6, A, B, E, G, H, I, K, M, N, O, R, S, Z), chosen for their tendency to become blotched with increasing weight (for example, E or A), or their capacity to be confused with other characters (for example, 1 and I, or O and 0). Thus, any given table was made of 1, 2, 3, 4 or 5 occurrences of a given target character and the completing number of distractor characters (99 to 95). Each target character could pseudo-randomly appear in any given contrast/weight condition, but was presented once and only once in each polarity.

Independent variables

There were 4 independent variables: 3 polarities (white, black or gray backgrounds), 2 contrast values (normal or low), 3 weights (heavy, normal or light) and 3 repetitions. Polarity, contrast value and character weight were blocked but counterbalanced on the subjects. The 3 repetitions of each experimental condition were blocked.

There were 2 dependent variables, the subject's response time and the difference between the number of occurrences of the target character and the reported number thereof. Results are presented on Figure 9. The ANOVA on the response time showed only 2 significant main effects and no significant interaction effect. There was an effect of the polarity (F(2,22) = 3.778, p = 0.038) where post-hoc pairwise comparison showed that response time was longer for the black background than for the white background. The gray background was not significantly different from, either the white, or the black background. The significant effect of the contrast (F(1,11) = 4.968, p = 0.047) showed that response time was longer when the contrast was lower. Lack of further significant results is probably due to the fact that the range of the weight values was purposefully chosen very small. Indeed, larger differences might have yielded significant effects but were of no interest within the context of our study. One should keep in mind that the goal of this experiment was to help the designer choose the correct value(s), not to prove the effect of a given factor.

Results

Figure

Pairwise comparison

At the end of the session, we displayed on the screen pairs of pseudo-words or numbers, on the same background, but using different weights. For each pair, subjects were asked to tell which seemed more pleasing and comfortable to read [START_REF] Thurstone | A law of comparative judgement[END_REF]. Results show that heavier and medium weights were preferred on black and grey backgrounds whereas medium and light weights were preferred on white background. In other words, if choosing only one weight value, the medium one is best to make reading comfortable regardless of the polarity.

DISCUSSION

In this study undertaken in the context of safety-critical systems and difficult environments, we integrated design, scientific models and experimental observations in order to elaborate typeface artifacts in a carefully controlled stepwise fashion. Mackay & Fayard [START_REF] Mackay | Natural Science and Design: A Framework for Triangulation Across Disciplines[END_REF] provided a framework for interfaces design, integrating research, engineering and design. They describe how interaction models can be created from theory and observations to instantiate new artifacts, ranging from early simulations to working prototypes to products. The design team must agree to work in a very interactive but constrained manner, each domain imposing or adapting its own rules and limits. In our study, design and typeface artifact constantly evolve from experimentations. To conceive the experiments, we had to operationalize the requirements of legibility with typographic properties and experimental questions. For example, testing robustness entailed manipulating the weight properties to ask if more pixels lead to better shape perception, especially in degraded environment (low contrast). Thus, needs, requirements and design choices are linked through quantified typeface parameters (for example, typographic contrast, weight, spacing…). With this method, designing takes time but yields a multi-layered product which can easily be further adapted, should the need arise.

Safety-critical context of use has driven our choice to go through iterations of short cycles of experimentation-based design in order to ensure conformity with previously defined requirements and design principles. These experiments were designed either to validate broad typographical choices or to fine-tune font properties.

Validating Design

Results from experiments 1 and 2, a comparison of font legibility, has shown that our basic prototype font does well with respect to the tested requirements of legibility (character recognition and discrimination) and robustness, and yielded better results than an in-use aeronautical font and the Verdana font. We conducted these experimental manipulations in order to validate our initial design concepts, first in a carefully controlled laboratory environment and, then, in a real but controlled cockpit environment. To our knowledge, the replication of laboratory experiment in an operational environment, as well as the transposition of laboratory experimental constraints to an "almost" real world cockpit setting is fairly innovative. It allowed us to quantitatively evaluate legibility and validate our results on the intended destination screen and in cockpit ergonomic context (pilot position, viewing angles and lighting). Indeed, this type of experiment should be replicated on the final product if one wants to definitely state its legibility as required.

Helping Design

Even though our font design was largely validated, the confusion matrices pointed to legibility problems for some character shapes. Confusion matrices reveal not only the localization but also the direction of asymmetric confusions. For example, in the 5 and S pair confusion, we found that the problem was rather with the drawing of "5" than that of the "S". Used on results from experiments geared towards design validation, confusion matrices nevertheless helped refine character shape.

Experiment 3 is but an example of the experiments currently carried out on the typographic properties of the prototype font, such as weight, slant, and spacing among others. Comparing instances of the prototype font designed with different values of one given property, has allowed us to build a range within which the effect of the values is known. Not only does it help to choose the best values for a given effect, but it also allows predicting with fair confidence the consequences on a given property to have to contend -for some reasons-with "less than best values". In other words, such fine-tuning of font properties serves to define a space of available choices, and their effects, for the design. In contrast with traditional end-user evaluations which strive to validate a finished product with respect to a definite set of specificities, our iterative evaluation process leaves room and direction for changes, should the requirements change. We can also use this range of values to ensure compliance across multiple requirements. For example, the manipulated range of available width helped design condensed shapes to address the text density of current cockpit interfaces.

Implications for HCI

The experimentation-based design process was necessitated by the safety-critical context of use. In mundane context, digital typefaces tend to be taken for granted. Reading is such an ubiquitous task that it is rarely tested as such.

Generally, text reading is the unquestioned input for a given tested interaction involving a widget, for example. The ensuing observed performance will be understood as a function of the widget. As long as text display and rendering conforms to set specifications, interfaces designers will probably not subject the chosen typefaces to the rigors of testing and evaluation they subject other aspects of interface design, let alone tinker with the typefaces. Reading is a task requiring cognitive resources and typeface legibility is bound to influence cognitive load.

Our results clearly show how minute design differences (such as half-bitting rendering technique) can influence character reading performance, even when comparing two typefaces, both aiming above all for legibility, such as Verdana and our prototype. Acknowledging the importance of typefaces and validating their usability should not be confined to safety-critical contexts. The ubiquity of text display in numerous interfaces and the multiplicity of contexts lead us to believe that the experimental verification of such typographical components in context of use is fundamental for interfaces design.

Figure : superposition of alphanumeric glyphs from 10

 10 Figure : superposition of alphanumeric glyphs from 10 readable fonts, right, glyphs "Q" and "3" details.

Figure 1

 1 Figure1was produced by superimposing the glyphs of ten digital fonts: Univers, Frutiger, Helvetica Neue, Vera Sans, Verdana, Lucida Grande, Myriad Pro, Calibri, Tiresias PC and Bleriot. Overlapping of glyphs shows a high overall similarity of forms, with some interesting variations for some signs, for example glyphs "Q" or "3" (details on Figure1). Proximity of the main typographical invariants values (weight, character width) of these fonts allows us to consider them as reference values for our experimental exploration of font properties.

Figure

  Figure : glyphs E, 0 and 1 from three tested fonts (from left to right, aeronautical, Verdana and prototype)

Figure : Experimentation 1 ,

 1 Figure : Experimentation 1, distribution of responses (averaged over all subjects) for subject/screen distance of 80 cm and 100 cm.

Figure : letter confusion

  Figure : letter confusion matrix (detail) for the prototype (100cm). Left column shows displayed characters; top row shows subjects' responses. Each intersection of column and row presents the number of occurrence of the stimulus/response pair.The correct responses are displayed on the diagonal of the matrix (stimulus "A" and response "A"...). All other cases are wrong answers, e.g. stimulus "5" and response "S". The far right column (on blue) presents the number of no-responses for each character.

Figure : Experimentation 2 ,

 2 Figure : Experimentation 2, distribution of responses (averaged over all subjects) for subject/screen distance of 80 cm and 100 cm.

  Figure : Experimentation 2, average response time for each font weight on 3 backgrounds with high or low contrasts.