Lorène Dubreuil
email: lorene.dubreuil@lurpa.ens-cachan.fr

Yann Quinsat
email: yann.quinsat@lurpa.ens-cachan.fr

Claire Lartigue
email: claire.lartigue@lurpa.ens-cachan.fr

IDMME -Virtual Concept -Improve -Ingegraf 2014 58 -1-Copyright of IDMME -Virtual Concept -Improve -Ingegraf Multi-sensor approach for multi-scale machining defect detection

Keywords: multi-sensor, digitalization, stereoscopic system, machining defect, sculptured surface 1-Introduction

Several measuring systems used in industries are most often used in a separated way and not efficiently. Multiscale multi-sensor measurements are nowadays challenging to improve quality and decrease measuring time. However, this requires that each class of defects can be link with the appropriate measuring system. This paper deals with a comparative study of several measuring techniques for the measurement of multi-scale machining defects. In particular, an attention is paid to a new measuring method based on stereo-correlation along with classical measuring technique such as laser scanner, touch probe and confocal interferometry. Considering some well-known defects, the comparative study assesses the ability of each system to measure a class of defects. This study constitutes the first stage towards the definition of a multi-sensor multi-scale measuring system.

forward an approach of optical sensor qualification aiming at the choice of the most appropriate measuring system according to the feature to be measured. The application is limited to standardized dimensional specifications. Several studies focus on multi-sensor measurement. Weckenmann et al. [START_REF] Weckenmann | Multisensor data fusion in dimensional metrology[END_REF] classifies multi-sensor measurement in three classes depending on how the sensor works (complementary, competitive or cooperative). The association of an optical sensor and a touch probe is especially explored. Chan et al. [CB1] associate a CCD camera to a touch probe in a complementary way to improve the accuracy and rapidity of the measurement, as well as Zexia et al. [START_REF] Zexiao | Complete 3d measurement in reverse engineering using a multi-probe system[END_REF] which employ a structured-light sensor. Martinez et al. [MC1] used competitively a laser scanning and a touch probe.

Few researches address the issue of multi-scale multi-sensor measurements. Actually, manufacturing parts that have to be measured generally present deviations relative to the nominal model induced by the process. These deviations are multiscales. Therefore, it seems necessary to adapt the measuring system with regard to its ability to locate or/and quantify deviations. However, it is not simple to directly associate the deviation to be evaluated with the appropriate measuring system. This issue is challenging. In this context, the present paper focuses on a study of feasibility of different measuring systems to measure specific deviations induced by machining. More particularly, the addressed deviations are those obtained during a 3-axis milling operation using a ball-end cutter tool (mismatches, scallop heights, overcut). Two different measuring systems are tested corresponding to two different measuring technologies. The first system consists of CMM equipped with a laser scanner (laser Kréon) mounted on an orientation head to increase the sensor accessibilities. The second measuring technique is the 3D--2-Copyright of IDMME -Virtual Concept -Improve -Ingegraf DIC system based on stereo-vision by image correlation. This technique is relatively new in the domain of dimensional metrology. The feasibility study is carried out thanks to a part which is defined in figure 1. The part is simple on purpose. On the one hand, classical deviations encountered during milling can be controlled, and on the other hand, the shapes are simple to measure. The part includes three different types of deviations: mismatches, scallop heights and overcuts. The test part is milled on a HSM (High Speed Machining) 3axis milling center according a back and forth parallel plane strategy. The finishing tool used is a 5 mm ball-end cutter. With such a strategy it is possible to simply control the height of the 3D topography (scallop heights) by controlling the distance between passes. Hence, 2 different topographies are defined for the tests (Rt1 and Rt2). The radius of the fillet that links the two cylinders of the part is equal to 4 mm. As the tool radius is equal to 5mm, a form error is generated on the fillet corresponding to an overcut during machining (∆Z1). Finally, to perform the mismatch, an offset by 0.1 mm following the Z axis (tool axis) is achieved during the milling (∆Z2). All the deviations aforementioned are summarized in figure 2. As the 3D-DIC system is new in dimensional metrology, the next section is dedicated to the description of this specific measuring method. The third section shortly details the measurement principle associated with the laser plane sensor (Kréon system). Measurement results and the feasibility study are addressed in section 4. Finally, conclusions and future works complete this study.

2-3D-DIC system with a mesh based approach 3D-DIC system is a stereoscopic measuring technique. The difference compared to photogrammetry or stereovision relies in the way of picture pairing. Indeed, picture correlation on speckled parts is the core of the method [START_REF] Hild | Digital image correlation[END_REF]. Nevertheless, as for any vision system, it requires a calibration procedure to identify the parameters of the model (which is classically a model). Several calibration methods may be considered as in [START_REF] Lavest | Quelle précision pour une mire d'étalonnage ?[END_REF], [B1], [BD1].

-Stereoscopic system model and calibration

A stereoscopic system permits to build 3D points from two 2D pictures. Figure 3 puts forward this principle. As it can be seen, 2 pictures are required in order to remove the ambiguity associated with a unique picture. Due to the projective transformation, a 2D point belonging to a picture corresponds to infinity of 3D points. For instance, in figure 3, the 2D point m in picture 1 could be anywhere on the 3D line ∆M. With a second camera, the intersection of the two lines of a same point will give the corresponding 3D point. However, a pairing technique has to be chosen to determine the same 2D points of the two pictures (m and p in the proposed example). The pairing technique used in the 3D-DIC measurement is the picture correlation. Let us detail in the following of this section, the pinhole model, the stereoscopic model and the calibration developed to perform 3D point measurements.

-Pinhole model

The pinhole model is a projection perspective model which allows us to express the 3D point coordinates defined in a reference frame in the picture frame. This consists of three geometric transformations [START_REF] Faugeras | Camera calibration for 3D computer Vision[END_REF], [T1] as defined in figure 4. The transformation between the world frame and the camera frame , consists of a rotation and a translation defined thanks to a homogeneous matrix (see Equation 1). The parameters associated with this transformation are called the extrinsic parameters.

[ ] = []. [ ] = [ 3 * 3 ] . [ ] (1)
The second transformation is a perspective projection of in the retinal plane . The last one is an affine transformation from the picture center to the picture

-3-Copyright of IDMME -Virtual Concept -Improve -Ingegraf corner . [ ] → [ ] → [ ] → [ ̃ ̃] → [ ̃ ̃]
Figure 4: Pinhole model of a camera.

The parameters associated with the matrix transformations and are called the intrinsic parameters as for the internal parameters (focal, pixel size and number, picture center). An additional transformation could be taken into account which corresponds to distortions of the camera. In this study, distortions are not considered. Both intrinsic and extrinsic parameters need to be identified. This is performed thanks to the calibration process.

-Calibration of the measuring system

The purpose of the calibration is to identify all the parameters of the pinhole model. Thus, the relationships between 3D points and picture points are assumed to be known (equation 2).

[ ̃ ̃ ] = [ ]. [ ] (2)
Lavest et al. [START_REF] Lavest | Quelle précision pour une mire d'étalonnage ?[END_REF] summarize all the mathematical procedure leading to camera calibration. Technically, a minimum number of points has to be known in the two frames ( and ) to achieve calibration. Several methods could be considered for this purpose. Bouguet [B1] achieves the calibration of the measuring system by shooting a well-known pattern, commonly a checkerboard pattern, in several positions. As the geometry of the pattern is supposed to be completely defined the intrinsic and extrinsic parameters can be calculated from equation 2. As this method requires numerous views of the checkerboard pattern according to different locations, acquisition time could be important.

-3D shape reconstruction

This section addresses the measuring method with the 3D-DIC system based on picture correlation once calibration has been performed. It is considered that the stereoscopic system is beforehand calibrated with the method proposed by Beaubier et al.

[BD1].

The method proposed in the paper has drawn on the prior work developed in [BD1] but uses mesh-based approach to represent the part shapes instead of the NURBS representation previously adopted. This enlarges the possibility of shape representation in particular noncontinuous in tangency surfaces can be easily described. Therefore, the parts are defined as mesh models which can be calculated from a CAD model. The minimization problem written previously in equation 4 becomes the problem linearized in equations 5 and 6 for which the unknowns correspond to the displacements of nodes of the mesh model .

= ∫ [ - + ∇ . -∇ . ]² ̃ ̃ (5) , = , (6)
In order to respect the mesh consistency, to avoid unexpected displacements and to reduce the number of unknowns, displacements are enforced along the normal vectors of the node. In figure 5, a mesh before and after displacement is

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presented. The initial mesh is pictured by nodes , the final mesh is represented by nodes ′ and the normal vectors are ⃗⃗⃗⃗⃗ . This method also involves displacement to be evaluated only in one direction and therefore computational time is reduced. Considering these displacement directions, equation 6 becomes equation 7 with the coordinate of nodes following its vector normal in the CAD frame.

, = , (7)
The vector normal to a node is evaluated as the mean value of the facets surrounding the node.

As deviations are small, the assumption of small displacements of nodes is adopted. This supposes that all the normal vectors at nodes are invariant whilst the reconstruction. To improve the resolution of the equation system, integration points are added on each facet as described in figure 6. Taking into account the addition of integration points in the algorithm, equation 7 becomes equation 8 with coordinates of integration points in the CAD frame.

, = , (8)

3-Laser scanning Kréon

This section introduces the measuring system also used to qualify the machined part. Laser scanners acquire a high density of point data with an acquisition time reduced. The principle of measurement is based on triangulation. Indeed, a laser plane is projected on the surface to be measured and its intersection (the profile stripe) with the surface is observed by a camera (figure 7). The coordinates of the profile stripe are determined thanks to triangulation (equation 9). The association of the laser scanner with a displacement system permits to measure the whole surface.

= * sin . sin sin + (9)

4-Measurement of the test part and results

This section deals with the results of the comparative study conducted to evaluate the ability of each measuring system to measure the deviations previously defined (see figure 2). To define a reference, the test part has been measured with a touch probe mounted on a CMM and the sensor Stil. These measurements are chosen as references and are compared to the measurements carried out with the laser scanner Kréon and the 3D DIC system (second part of this section). Finally, the feasibility study is performed.

-First measurements of the test part

A first measurement of the part is performed to stand for the reference. Macro-defects are measured with a touch probe (Renishaw TP2 stylus), mounted on a CMM while the microdefects are measured thanks to the Stil sensor. Touch probe measurement is commonly used in dimensional metrology due to its high accuracy. However, its use is limited to inspection of known surfaces (prisms, cylinders, etc.) which requires lower data density. Other limitations are the accessibility of the touch probe which is impossible in areas smaller than the diameter of the tip ball.

Based on the chromatic confocal sensing technology, the sensor Stil evaluates the surface topography at micro-scale.

A study conducted by Quinsat and Tournier [START_REF] Quinsat | In situ non-contact measurements of surface roughness[END_REF] put forward that this sensor, used in a machine tool, is able to discriminate the surface topography evolution during machining and polishing.

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The measured features acquired with the touch probe are the different cylindrical surfaces (convex and concave) presented in figure 9. The measurement of the three planes , and , allows the determination of a reference frame. This frame permits to analyze the coordinate Z of the measured data and to evaluate ∆Z1 and ∆Z2 in figure 2. The points collected are treated thanks to the workspace "Quick Surface Reconstruction" of Catia V5. To each point cloud corresponding to a feature, a cylinder is associated via the module "Basic Surface Recognition" considering that for each one the radius and the axis are imposed. Indeed, it leads to evaluate the deviation following the Z axis corresponding to the displacement of the tool axis (see figure2). Results are displayed in table 1.

Micro-scale geometries are acquired with the STIL sensor. In particular, this sensor is well-adapted to measure the mismatch as well as the 3D topographies induced by ball-end milling. The mismatch is presented in figure 10; figure 11 illustrates an example of scallop height. Mismatch (∆Z2) is evaluated thanks to the analysis software Mountains Map on a measured profile as in figure 10 as well as Rt1 and Rt2 which are evaluated directly on the extracted profile as for instance in figure 11. Results are summarized in table 1.

-Comparative study

Measurements proposed in the previous section give a reference for the errors to be evaluated. These results are compared to those obtained with the two measuring systems (Kréon and 3D-DIC). Measurements are analyzed in the same way and are displayed in table 1.

With regards to the Kréon system, it has been chosen to scan the surface with only one orientation of the laser in order to avoid overlapping errors generally appearing when using multiple sensor orientations. Based on the ICP Algorithm (Iterative Closest Point) a registration of the digitized point cloud is performed. Results from are given in figure 12 by the mapping of the deviations between the CAD model and the measured point cloud. By analyzing this mapping, overcut and mismatch are easily identified; contrary to scallop heights which are not observed. Following this measurement, only the mismatch and the overcut can be thus quantified with this measuring system. With such a system, it is not possible to quantify the value of the scallop height. In table 1, the value of the deviations following Z axis obtained with the Kréon system are compared to those obtained previously with the touch probe TP2 and the sensor Stil.

To achieve 3D DIC, a black and white random pattern is projected onto the test part, and two pictures are recorded. The calibration of the stereoscopic system is achieved thanks to the CAD meshed model. In figure 14 the residual following the calibration is observed. Locations of deviations are putted forward to the places for which the residual increases. For instance, the overcut in the center of the study part is easily identifiable in figure 14. Therefore, the study only concerns the overcut on the fillet (Cyl2 in figure 9). The objective is here to reconstruct the 3Dshape using the method detailed in §2.2 by node displacements. Figure 15 displayed the values of the residual on the fillet before and after node displacements with 3D-DIC. A global decrease can be observed. It is thus possible to evaluate the value of the overcut. Results relative to values of the defects obtained with 3D-DIC are summarized in table 1. . Table 1 enhances the capability of a measuring system to evaluate a class of defect. Crossed boxes put forward incompatible couples (defect/measuring system). Concerning the crossed boxes of the Kréon ant the 3D-DIC, the amplitude of the defects is of the same order as the measurement noise. The touch probe is not able to acquire surface topography. Finally, the measuring range of the sensor Stil is smaller than the size of the overcut ∆Z1.

-Feasibility study

As might be expected, only the sensor Stil is able to detect micro-defects. Therefore, it remains the measuring system the most adapted to evaluate 3D topographies.

The system Kréon turns out to be a good solution to measure macro-defects within a large range. Indeed, results obtained with such a system a comparable to those obtained with the TP2 reference system for the overcut (of 2 mm) as well as for the mismatch (of 0.1 mm). This makes the choice of this sensor particularly relevant for this class of defects considering acquisition time and the high density of the acquired points. The 3D-DIC measuring system only provides a result for the overcut defect, but the value remains distant from the reference value. This method needs to be improved in future works to be usable to quantify defects with a better accuracy. However, this method provides a very smart, simple and fast method to locate macro-defects by an analysis of the residual as shown in figure 14. Therefore, once the defect is located, another system (such as TP2 or Kréon) more accurate can be used in a complementary way to quantify the value of the defect.

6-Conclusions and future works

The aim of the paper was to study the feasibility of measuring systems to measure specific defects. The study is carried out on a test part including classical defects encountered during milling (mismatch, form error, scallop height), with the objective of linking the characteristic to be measured with the appropriate measuring system. The study addressed to particular system: a commonly used laser-plane scanner Kréon, and a new system, 3D-DIC, based on stereocorrelation, Results have highlighted that the system Kréon is the most efficient measuring system for the majority of the macrodefects. On the other hand, 3D-DIC seems to be useful to locate deviations on a part. Indeed, this study shows that deviations lower than 0.1 mm cannot be identifiable due to high noise measurement, contrary to larger deviations which are easily locate but not yet quantifiable. As expected, microdefects are only measurable thanks to appropriate system to micro-geometry measurements such as the Stil sensor. This study enhanced the need of complementary multi-system measurements within a multi-scale multi-sensor context.

In the aftermath of this study, a multi-scale multi-sensor measuring system could be imagined. A choice on the way of how the sensor works [START_REF] Weckenmann | Multisensor data fusion in dimensional metrology[END_REF], will have to be established, to carry out an efficient multi-scale multi-sensor measuring system.

7-References

[AM1] Audfray, N., Mehdi-Souzani, C., and Lartigue, C. (2012). Qualification et performances des systèmes de mesure optiques : Qualipso. [CB1] Chan, V., Bradley, C., and Vickers, G. (2001). A multi-sensor approach to automating coordinate measuring

Figure 1 :

 1 Figure 1: CAD model and example of tool path of the study part.

Figure 2 :

 2 Figure 2: Diagram of the deviations applied to the test part Whatever the technology used, the deviations are obtained by measuring a collection of 3D points on the part surfaces. It is thus necessary to present the stage of point measurement for the three measuring systems considered.As the 3D-DIC system is new in dimensional metrology, the next section is dedicated to the description of this specific measuring method. The third section shortly details the measurement principle associated with the laser plane sensor (Kréon system). Measurement results and the feasibility study are addressed in section 4. Finally, conclusions and future works complete this study.

Figure 3 :

 3 Figure 3: Stereoscopic principle with 3D point construction from two pictures.

Figure 5 :

 5 Figure 5: Principle of displacement of nodes along their normal vectors.

Figure 6 :

 6 Figure 6: Discretization of a facet in integration points.

Figure 7 :

 7 Figure 7: Triangulation principle of the laser scanner.Nevertheless the laser scanner has several disadvantages, such as a limited viewpoint, sensitiveness to the optical conditions, digitizing noise and overlaps due to the necessity of several sensor orientations. The accuracy of the sensor is related to many factors: relative position between the sensor and the measured surface, view angle, surface conditions, etc. [AM1]. Studies have enhanced that the best conditions of scanning is obtained with a unique orientation of the laser scanner. Under these conditions, the measuring system accuracy can be assessed thanks to quality indicators: a noise of 9 µm and a trueness of 2 µm/mm [AM1].

Figure 9 :

 9 Figure 9: Features identification on the study part.

Figure 10 :

 10 Figure 10: Mismatch (∆Z2) measurement with the chromatic confocal sensor Stil.

Figure 11 :

 11 Figure 11: Scallop height (Rt1) measurement with the chromatic confocal sensor Stil.

Figure 12 :

 12 Figure 12: Mapping of deviations between the CAD model and the point cloud acquired by the Kréon after ICP registration.

Figure 14 :- 6 -

 146 Figure 14: Residual (%) on the test part after calibration of the stereoscopic system.

Figure 15 :

 15 Figure 15: Residual (%) on the fillet before and after node displacements.

[ B1 ]

 B1 Bouguet, J.-Y. (2010). Camera calibration toolbox for matlab.http://www.vision.caltech.edu/bouguetj/calib_doc/ind ex.html [BD1] B. Beaubier, J.-E. Dufour, F. Hild, S. Roux, S. Lavernhe and K. Lavernhe-Taillard. (2013). CAD-based calibration and shape measurement with StereoDIC. Experimental Mechanics [BU1] Basilio Ramos Barbero and Elena Santos Ureta. Comparative study of different digitization techniques and their accuracy. Computer-Aided Design, 43(2):188 -206, 2011.

  This conservation is carried out only if the exact calibration parameters are known. As it is seldom the case, a global formulation of the sum of squared differences over the region of interest ( ) is expressed in equation 4.

	=			(3)
	= ∫ [	-	]² ̃ ̃	(4)
	By minimizing the correlation residual , calibration
	parameters are obtained. Contrary to the method proposed by
	Bouguet, this one only uses two pictures; acquisition time is
	thus reduced.
	Another technique for extrinsic parameters identification
	relies on feature recognition such as lines or circles.
	Knowing the CAD model of a part with specified features, it
	is possible to associate a feature in a picture to the same
	feature in the CAD model. As this technique does not lead to
	intrinsic parameters, it only can be complementary to the
	previous one [B1]. The use of the two calibration methods in
	a complementary way permits to maximize the benefit of
	each one.
	Another method puts forward by Beaubier et al. [BD1], offers
	a new technique of calibration based on stereo-correlation. The
	particularity of this method is that the object leading to the
	calibration will no longer be a calibration pattern but directly
	the test part and its CAD model. The CAD model is more

specifically a NURBS model of the test part. Hence, links between picture frames and 3D frame is virtual because the 3D frame is the CAD frame. The pairing technique is the picture correlation. The pictures shot by the left and right cameras are respectively denoted by and , where = ̃, ̃ and = ̃, ̃ . Conservation of the gray scale for both pictures yields equation 3.

Table 1

 1 summarizes all the results: those obtained with the two measuring systems (Kréon, 3D-DIC) we want to assess and the reference measurements (TP2 and Stil). After surface association to each point cloud corresponding to a feature via the module "Basic Surface Recognition" of Catia V5, ∆Z1 and ∆Z2 are evaluated and displayed in table 1.

	Deviations Overcut ∆Z1 (mm) Mismatch ∆Z2 (mm)	TP2 2.077 0.111 0.097 0.118 Stil Kréon 3D-DIC 2.059 1.934
	Scallop height 1 Rt1 (µm)	11.9
	Scallop height 2 Rt2 (µm)	5.32

Table 1 : results.

 1


Sergi Pujades

Frédéric Devernay

VIEWPOINT INTERPOLATION: DIRECT AND VARIATIONAL METHODS

Keywords: Viewpoint interpolation, image-based rendering, blending factors, variational method

We address the topic of novel view synthesis from a stereoscopic pair of images. The techniques have mainly 3 stages: the reconstruction of correspondences between the views, the estimation of the blending factor of each view for the final view, and the rendering. The state of the art has mainly focused on the correspondence topic, but little work addresses the question of which blending factors are best. The rendering methods can be classified into "direct" methods, defining the final image as a function of the original images, and "variational" methods, where the synthesized image is expressed as the solution minimising an energy. In this paper, we experiment different combinations of the blending factors and the rendering method, in order to demonstrate the effect of these two factors on the final image quality.

INTRODUCTION

Novel view synthesis from a stereoscopic pair of images has been extensively studied, for example for content creation for glasses-free 3D displays from binocular stereoscopic content. Those techniques proceed in general in 3 stages: the estimation of correspondences between the novel and the reference views, the estimation of the contribution (or weight) of each view in the final view, and the rendering method. The stereo correspondence estimation problem has been largely explored [?], but few works have formally studied which is the "correct" leverage between the contributions of each view. We will call this leverage the "blending factors" of each view. The most common blending factors considered in the literature are the local deformation of the image introduced by the change in the view point, and the distance between the new view and the reference ones. Yet, several questions arise: How is each blending factor choice formally supported? How does the synthesized view quality depend on these blending factors? Ultimately, what blending factors should be preferred?

In the view interpolation domain, methods can be clustered in 2 groups. The "direct" methods and the "variational" methods. Most state of the art methods are direct: the color of a pixel in the final image is given as a function of the colors of the corresponding pixels in the reference images. In the variational methods, the final image minimises an energy corresponding to a maximum a posteriori, often derived from a generative model. Using the Bayesian formalism, the blending factors between the views can be formally derived. However, those optimization techniques require heavier computations than the direct ones. We would like to know if the results obtained with these methods compensate for their computational complexity. In this article we propose a study to analyse the impact of the blending factors and the used method in the final result. We evaluate those methods on Lambertian and non-Lambertian scenes in order to see, in which case, which choice is better.

PRIOR WORK

Viewpoint interpolation methods belong to the largely studied field of image-based rendering [START_REF] Shum | Image-based rendering[END_REF]. Unstructured Lumigraph [START_REF] Buehler | Unstructured Lumigraph rendering[END_REF] introduces the desirable properties an ideal image rendering method should have: "use of geometric proxies", "unstructured input", "epipolar consistency", "minimal angular deviation", "continuity", "resolution sensitivity", "equivalent ray consistency", and finally "real-time". Moreover they state the weight of each reference image when rendering the final view. Authors also present a direct method taking into account all this desirable properties. The "minimal angular deviation" is measured with the angles between the optical rays of the rendered and reference images. The "resolution sensitivity" is enforced by computing an approximation of the Jacobian of the planar homography between the rendered and the reference image. The balance between this factors is adjusted depending on the scene. Precisely, "resolution sensitivity" has in most experiments a tiny weight compared to the "minimal angular deviation". We would like to put forward the influence of those weights in the final result.

Methods addressing the problem of view interpolation from a stereoscopic pair of images use two blending factors: most of them consider the normalised distance α between

D C 1 C 2 P α 2 α 1 D C 1 C 4 P α 1 C 2 C 3 α 2 α 3 α 4
Fig. 1. Rendering view D from C i using [START_REF] Wanner | Spatial and angular variational super-resolution of 4D light fields[END_REF]. Left: resolution sensitivity will prefer C 2 to C 1 , even-though angular distance would prefer C 1 over C 2 . Right: flat scene parallel to views: all views will have the same blending factor, eventhough their angular distance is different for each of them.

the new image and the reference image. The two associated blending factors are α and (1α) [START_REF] Hong | Fast view interpolation of stereo images using image gradient and disparity triangulation[END_REF][START_REF] Smolic | Intermediate view interpolation based on multiview video plus depth for advanced 3D video systems[END_REF][START_REF] Devernay | Novel view synthesis for stereoscopic cinema: detecting and removing artifacts[END_REF]. Other methods measure the deformation of the image [START_REF] Lhuillier | Image interpolation by joint view triangulation[END_REF], using the Jacobian of the planar homography between the rendered image and the reference image. While addressing the super-resolution problem, Wanner and Goldluecke [START_REF] Wanner | Spatial and angular variational super-resolution of 4D light fields[END_REF] propose a very general variational method to generate images at new viewpoints. They present a generative model describing the image formation process and establishing the energy corresponding to its maximum a posteriori, using the Bayesian formalism. This formalisation brings them to derive the blending factor of the images to be given by the determinant of the Jacobian of the transformation between the final image and the reference one. While these blending factors take into account the "resolution sensitivity", the "minimal angular deviation" is overlooked. It doesn't appear in the equations and Fig. 1 illustrates two configurations showing the contradictions with [START_REF] Buehler | Unstructured Lumigraph rendering[END_REF].

Alternative methods are proposed by [START_REF] Yan | Depth mapping for stereoscopic videos[END_REF][START_REF] Lang | Nonlinear disparity mapping for stereoscopic 3d[END_REF] based on the deformable meshes from Gal et al. [START_REF] Gal | Featureaware texturing[END_REF]. Their main hypothesis is that artifacts introduced by mesh deformations are visually more acceptable than those produced by image blending. However, in case of important deformations of the images, it would be interesting to merge two images generated with these techniques. Unfortunately this question is avoided in their works.

So, in the literature different blending factors are used, but to our knowledge, there is no study directly comparing their performance.

VIEWPOINT INTERPOLATION METHODS

All methods will have the same input: a rectified pair of stereoscopic images, 2 disparity maps with the correspondences between the views, and a value α ∈ [0, 1] corresponding to the position between the reference views to be rendered, being 0 the left image position, and 1 the right image position.

Direct Methods

The direct methods first compute the inverse transformations going from the final image to each reference image using the disparity maps and the α value. Pixels without a correspondence are labeled as invalid. This typically happens at disocclusions. The final image is generated using the color of the corresponding pixels in the reference images, and using a linear interpolation if coordinates have floating point precision.

We have chosen to study 4 different weights for the blending factors. First we consider the "classic" weight ((1α), α) taking into account the "minimal angular deviation". The second weight also fulfills this property. It is ((1α) 2 , α 2 ). The third chosen weight ignores the "minimal angular deviation" and assigns to each image the same weight. This is done independently of the α value and the local deformation of the image transformation. The fourth weight is proportional to the local deformation of the transformation of the image, as described in [START_REF] Wanner | Spatial and angular variational super-resolution of 4D light fields[END_REF], |detDτ | -1 . In our case τ is the transformation given by the disparity and we compute its deformation with finite differences. In all 4 cases weights are normalized so that their sum is 1. If one of the two corresponding pixels is marked as invalid we assign a 0 weight to it, and a 1 weight to the other pixel. If both corresponding pixels are invalid, we mark the pixel as invalid. If one or both of the corresponding pixels are valid, we assign to the final pixel the weighted sum of the values. Notice that at this stage some pixels of the rendered image are labeled as invalid. We explain how we handle those cases in section 3.3. Fig. 2. Example images from the datasets: "aloe" from [START_REF] Hirschmuller | Evaluation of cost functions for stereo matching[END_REF] and "tarot", "bracelet" and "amethyst" from [START_REF] Vaish | The (New) Stanford Light Field Archive[END_REF]. 1. Numerical results of the comparison between real and rendered images for the datasets "tarot" and "bracelet". For each view and method we present PSNR in dB (the bigger the better the signal) and DSSIM scaled with 10 -4 (the smaller, the most similar the images are). Views (2, 3, 14 and 15) are close to the reference views. Views (8 and 9) are central viewpoints.

The best value for each view is in bold, and the worse in italic.

Variational Methods

Variational methods find the image minimising an energy. Those energies have often two parts: the data term and the regularizer.

E(u) = E data (u) + λE prior (u). (1)
In the Bayesian formalism, the first term can be obtained by modeling the image formation process. A common hypothesis is to consider the sensor noise as a zero mean Gaussian. Its maximum a posteriori energy matches the minimum of a least squares overdetermined system. To write E data (u) we note the final image as u, the reference image i as v i , the definition domain of the images as Ω i . m i is a binary operator telling if the pixel is visible in the final image and τ i the transformation from the reference image i into the final image. ω i is the weight of the pixels of image i. Then

E data (u) = n i=1 1 2 Ωi ω i m i ((u • τ i ) -v i ) 2 . ( 2
)
For the variational methods we have chosen to use two different weights. The first is the one proposed by [START_REF] Wanner | Spatial and angular variational super-resolution of 4D light fields[END_REF] corresponding to the deformation of the transformation of the images:

ω i = |detDτ i | -1 (3)
The second weight is the "classic" ((1α), α), taking into account the "minimal angular deviation". Although this second weight is not formally derived from a known generative model, the energy is well defined and can be minimized. Again, all weights are normalized so that their sum is 1.

Prior or regularizer

In the Bayesian formalism a prior is used in order to decide in cases where no information is available for some areas, or when several candidates for a solution are possible. In the direct methods this phenomena also arises if none of the reference images can propose information for the desired area. A "classical" prior in computer vision is the total variation [START_REF] Leonid I Rudin | Nonlinear total variation based noise removal algorithms[END_REF]: E prior (u) = Γ |Du| . It has the important property to provide a convex energy and to be well suited for the gradient descend minimization techniques. In the direct methods, we fill the remaining invalid pixels with a hole filling technique to propagate valid information from the nearest neighbors. Its behaviour is similar to the role played by the prior [START_REF] Leonid I Rudin | Nonlinear total variation based noise removal algorithms[END_REF] during the minimization, so it seems a fair choice in order to provide a reasonable comparison. We highlight that our goal is not to obtain the best possible images, but to provide a fair comparison between "direct" and "variational" methods.

Experiments

In order to compare the different methods and the impact of the blending factors in the final result we have used multiple datasets from the "Middlebury Stereo Dataset" [START_REF] Hirschmuller | Evaluation of cost functions for stereo matching[END_REF] and the "Stanford Lightfield Archive" [START_REF] Vaish | The (New) Stanford Light Field Archive[END_REF]. Fig. 2 shows examples of the used images. The first one proposes very lambertian scenes (color does not depend on the viewing angle). Each scene has 6 aligned views. We use the most distant ones (1 and 6) to generate the other 4. The second database provides more challenging scenes, including highly specular reflections, transparencies and inter-reflections. Each dataset has 256 view per scene arranged in a regular 16x16 grid. We have selected the central line (the 8th) and used its most distant viewpoints (1st and 16th) to generate the other 14. This way we can compare the original images with the generated ones. To do so we have used two state of the art measures.

The "Peak Signal to Noise Ratio" (PSNR), in dB, the bigger, the better is the signal. And the "Structural SIMilarity" (SSIM) developed to measure the visual similarity between two images. We report results with a distance based on SSIM:

DSSIM = 1-SSIM 2
, having no units. The smaller, the more similar are the images.

For the study we have used standard methods for the disparity maps computation [START_REF] Sizintsev | Coarse-tofine stereo vision with accurate 3d boundaries[END_REF] and [START_REF] Hirschmuller | Accurate and efficient stereo processing by semi-global matching and mutual information[END_REF]. Disparity maps obtained with [START_REF] Hirschmuller | Accurate and efficient stereo processing by semi-global matching and mutual information[END_REF] are not dense but we have completed them using the hole filling technique in [START_REF] Sizintsev | Coarse-tofine stereo vision with accurate 3d boundaries[END_REF]. The λ parameter in eq. 1 was empirically set to 0.15 for all experiments.

Results

We present the obtained results for the datasets "tarot", "bracelet" and "amethyst", using the disparities computed with SGBM [START_REF] Hirschmuller | Accurate and efficient stereo processing by semi-global matching and mutual information[END_REF]. Results with dataset "aloe" of "Middlebury Dataset" are very similar to those from "tarot" and are not presented. Results obtained with disparities computed with [START_REF] Sizintsev | Coarse-tofine stereo vision with accurate 3d boundaries[END_REF] are very close to the presented ones and are skipped.

Input images are coded in sRGB space. It is advised to convert them into RGB-linear when operating with pixel values. We tested using the sRGB and the linear versions and very similar results were obtained. Running times for direct methods are around 1 30 s for 1024x1024 images (real-time). Variational methods were solved using a gpu implementation of FISTA [16, ?]. Running time was about 1s for 1024x1024 images (not real-time).

Dataset "tarot" has a crystal ball with transparencies, violating the lambertian model. However colors on the rest of the scene do not change from one view to the other. Dataset "bracelet" has some specualr highlights on the metal, but the color difference between the left and right views is very small. Dataset "amethyst" is more complex. It has inter-reflections and highlight effects.

In Tab. 1, the difference between the methods for a fixed scene is small. PSNR and DDSIM values are very close.

In "bracelet", results of view 2 and 15 are slightly better when taking into account the "minimal angular deviation" (α, (1α)) and (α 2 (1α) 2 ) both in direct and variational methods. This was expected as those methods are capable of better rendering the highlights. However the improvement dissipates quickly as we render the next views (3 or 14). No significant difference between the direct and variational methods can be reported.

Notice how PSNR values on Tab. 1 ("tarot" and "bracelet") and Tab. 2 ("amethyst") are on the same order of magnitude; but DSSIM values are higher on Tab. 2 than on Tab. 1. We believe that this difference appears due to the fact that the scene is more complex, together with a greater capability of the DSSIM measure to compare the visual quality. Again, for each view, tendencies are similar as in Tab.1. However we report a significant difference between the DDSIM values of direct and variational methods. For complex scenes, variational methods are capable of better reconstructing the structure of the image.

DISCUSSION AND CONCLUSION

In this paper we have presented a study of the influence of the blending factors and the method in the result of the viewpoint interpolation techniques. We have compared several blending factors and two groups of methods, direct and variational. Conducted experiments show that for lambertian scenes, the choice of the blending factors has insignificant impact. Moreover, results obtained with direct or variational methods are equivalents, so direct methods should be preferred thanks to their simplicity. In the non-lambertian scenes, the choice of the blending factors considering the "minimal angular deviation" produce slightly better results with both direct and variational methods, although the improvements are only visible when rendering new images close to a reference view. However, the variational methods are capable of better render the structure of the image, obtaining improved results. In this case variational methods considering "minimal angular deviation" should be preferred.

In future work it would be interesting to continue this study for more general configurations: multiple input views and general position of reference and final view.

Table 2 .

 2 Numerical results for the dataset "amethyst". Same measures as in Tab 1 are displayed.

	AMETHYST	view 2	view 3	view 8	view 9	view 14	view 15
	Direct Methods
	α(1 -α)	33.84 1247 32.67 1265	30.66 1292 30.88 1299	33.60 1305 34.86 1305
	α 2 (1 -α) 2	33.81 1255 32.61 1282	30.69 1294 30.84 1300	33.42 1325 34.79 1313
	Constants	32.16 1218 31.62 1239	30.63 1288 30.91 1294	32.67 1273 33.13 1274
	Deformation	31.56 1239 31.07 1259	30.27 1307 30.54 1313	32.00 1293 32.36 1296
	Variational Methods
	α(1 -α)	32.80 1093 31.39 1116	30.30 1160 30.66 1168	33.77 1142 34.98 1141
	Deformation ([7])	31.87 1107 30.96 1126	30.27 1163 30.63 1170	33.01 1150 33.68 1152

This work was done within the Action 3DS project, founded by the French Caisse des dépôts et consignations


Bai Xue

Bo Fan

Xianghua Zhang

Yves Quiquempois

Gilbert Martinelli

Laurent Calvez
email: laurent.calvez@univ-rennes1.fr

Second-harmonic generation in chalcogenide glass-ceramic doped with CdS nanocrystals

Keywords: Optical materials and properties, Amorphous materials, Nanocrystalline materials, Sintering

An innovative way is proposed here to synthesize chalcogenide glass-ceramic by hotpressing a combination of Ge 20 Sb 12 S 68 glassy powder and non linear CdS nano-particles. The cadmium sulfide nano-particles, which possess second-harmonic generation property, were synthesized from basic cadmium solution strongly complexed by amine. The obtained glassceramics present homogeneous distribution of the crystals. The transmission reaches 30% at 5 µm and up to 60% at 10.6 µm. Second-harmonic generation at 0.9 µm has been detected. This technique can overcome the uncontrollable hetero-crystallization which tends to occur in the glass-ceramics prepared by the conventional thermal treatment method.

Introduction

Chalcogenide glasses are usually polarized by various manners to generate SHG [1,2].

The generated susceptibility (2) does not remain constant and decays over time. However, thermal treatment [3] is another route to obtain permanent SHG due to the presence of nonlinear crystallites within glassy matrix.

CdS crystal owns a large second-order optical non-linear coefficient (+44 12.6 pm/V at 1.064 µm) [START_REF] Weber | Handbook of Optical Materials[END_REF][START_REF] Miller | [END_REF]. Chalcogenide glass GeS 2 -Ga 2 S 3 -CdS [6] was studied to induce permanent second-order non-linearity in glass-ceramics containing CdGa 2 S 4 crystallites with a (2) estimated to be 38.85 pm/V [6]. But the second-order optical non-linear coefficient is only generated from a crystallized surface layer of about 15 µm which is difficult to control and induce strong scattering losses. Another study concerning the addition of metallic cadmium in the Ge 25 Sb 10 S 65 [7] base glass to generate non-centro-symmetric CdS micro-crystals indicates that the Cd 4 GeS 6 phase is preferentially instead of CdS by using thermal treatment. So far, no publications have reported glass-ceramic with permanent SHG signals only caused by the presence of non-linear crystals homogeneously dispersed. Since CdS crystals are difficult to make by conventional thermal annealing, new techniques are required to synthesize glassceramics with unique CdS crystals homogeneously dispersed in the matrix.

In this report, a new way to synthesize chalcogenide glass-ceramics is put forward, focused on chalcogenide glass-ceramic presenting second-order non-linear susceptibility attributed to the doping of CdS nanoparticles. Moreover a specific glass composition (Ge-Sb-S) possessing a wide transparency range and a close refractive index to that of CdS has been chosen to limit the scatterings and optical losses. Glassy powder and CdS powder were thoroughly mixed using a planetary miller and sintered by hot-pressing under vacuum.

Second-order non-linear signals can be detected upon these glass-ceramics.

Experimental

Characterization: Differential Scanning Calorimeter (DSC TA Q20) was used to determine the characteristic temperatures. Morphology images were recorded by Scanning Electronic Microscope. Crystal structure of the pellets was characterized using a Panalytical X'PERT Powder diffractometer operating with Cu K radiation. Transmission spectra were recorded by a double-beam spectrophotometer Perkin Elmer Lambda 1050 UV/VIS/NIR URA and by a Bruker Vector 22 spectrophotometer in the mid-infrared region. The second-harmonic generation at 0.9 µm was carried out by a Maker fringe method using an optical parametric oscillator (OPO, =1.8 µm) as the light source. Detailed information of the measurement was described in previous reports [7].

Synthesis of CdS powder:

CdS powder was synthesized from basic cadmium solution strongly complexed by amine [8]. The formula of the reaction is as follow:

2 3 2 2 3 2 2

Cd CH CSNH H O CdS CH C O NH H

CdS was synthesized in a 500-ml beaker and be stirred at room temperature by magnetic stirring to obtain crystals of homogenous size. The solution was prepared from the solutions to be 0.5 mol/L in CH 3 CSNH 2 , 1 mol/L in NH 4 Cl, and 0.1 mol/L in CdCl 2 . The pH was adjusted around 9.5 [9]. After 40-hours reaction, the turbid liquid was centrifuged to precipitate rapidly, that could prevent the aggregation during long time aging. At last, the precipitates were washed with deionization water and ethanol.

Glass synthesis:

The glassy matrix Ge 20 Sb 12 S 68 has been chosen as it presents a moderate glass transition temperature (270°C), a low band-gap of 550nm and a refractive index of 2.28 (2.35 for CdS).

The glass was synthesized by conventional melt-quenching method. High purity raw elements Ge (5N), Sb (5N) and S were used. Sulfur was purified by distillation to remove the residual impurities (O-H, C…). Raw elements were transferred into a 9-mm diameter silica tube, which was sealed under a vacuum (10 -3 Pa). Then, the tube was heated to 850°C and held for about 12 hours before being quenched in water until room temperature. The glass was broken and milled into powder using a planetary grinder (PM100 from Retsch) in a glove box under argon to avoid air pollution.

Preparation of glass-ceramics:

The CdS powder (10 mass%) was mixed with the Ge 20 Sb 12 S 68 glassy powder (90 mass%) in ethanol and stirred to well homogenize the mixture. The mixture was stirred until the ethanol was fully evaporated and then dried in an oven at 70°C for 12 hours to volatilize the residual ethanol.

The mixture was sintered by hot-pressing (HP) with a home-made equipment [10]. A stainless steel mold with an inner diameter of 20-mm was used. The hot-pressing at T g +100°C was performed under a primary vacuum using a load of 31 MPa. The procedure lasted for various durations. Then the sample was slowly cooled down to room temperature to relax the inner constrains.

In parallel, one sample was synthesized by re-melting the entire mixture in a sealed silica tube under vacuum at 750°C for 5 hours to test the possibility to prepare controllable glass-ceramic by the usual melt-quenching process.

Results and discussion

Two samples were sintered by HP using the sintering parameters listed in Table 1. The sample made in silica tube is denoted as CD3. To well detect the signals, glass-ceramic slices were then polished to reach a thickness of 0.5-0.7mm.

XRD patterns of the initial powder and glass-ceramics are shown in Fig. 1. Synthesis made at high temperature by sintering (CD2) or by melting (CD3) can lead to a reaction between the glassy matrix and CdS crystals which results in the formation of another crystalline phase Cd 4 GeS 6 [7]. However, the pure CdS phase can still be found in sample CD1 sintered at a lower temperature.

As shown in Fig. 2, samples CD1 and CD2 are black instead of red. Even if the sample CD3 is red colored, it is not transparent for the naked eyes due to strong light scatterings.

Moreover, strong impurity absorption peaks, such as O-H, S-H and H 2 O, are present in all samples. These impurities directly come from non-purified CdS under H 2 S flow and the use of ethanol which helped to homogeneously mix the CdS crystals with the glassy powder.

As observable in Fig. 2, optical signals before 1µm can be partially detected through CD1 and CD2 samples. These scatterings could be attributed to the defects (e.g. the pores)

and to CdS particles in the samples shown in Fig. 3 (a) and (b). Lower sintering temperature induces residual porosity which strongly affects the transmittance even with longer duration.

Moreover the use of a reducing atmosphere (vacuum) can strongly impact the behavior of sulfur within the glassy matrix potentially leading to the dark coloration of the samples. Fig. 3 (a) presents the interface between the glassy matrix and the crystals. Fig. 3 (b) shows that the glass does not fill in perfectly the crystals aggregate. In fact, among the crystals, pores can be seen, demonstrating that a temperature of 380°C is not sufficient to make the viscous glass flows all around the crystals. Different refractive index at the interfaces between holes/crystals/glassy matrix can also causes strong scatterings at short wavelength.

As observed in Fig. 3 (c) and (d), a higher temperature of sintering used for CD2 enhances the densification of the material, reducing the scatterings by lowering the residual porosity. However higher sintering temperature leads to the formation of heterogeneous CdS and Cd 4 GeS 6 crystals in the matrix (see Fig. 1). Even with a better densification, the uncontrolled growth of crystals leads CD2 sample to be less transparent than CD1 as shown in For the moment, the transmittance at 0.9 µm is so low that almost 90% of the signal is absorbed which makes an absolute estimation of the real susceptibility very difficult.

Improvement of the transmission at short wavelength or even at mid IR range by improving the sintering process will be necessary to make more efficient the generation of non-linear signals. Nevertheless, this innovative way of making glass-ceramics appears as a very interesting ways to prepare non conventional glass-ceramics. New challenges have to be overcome to enhance their transmittance both in visible and mid-IR ranges.

Conclusions

In this paper, we proposed a new way to synthesize efficient glass-ceramic by sintering the chalcogenide glassy powder doped with CdS nano-particles. Glassy powder and CdS nano-particles were thoroughly mixed and sintered by HP into a disc. The obtained slices present a pretty low transmission in the mid-IR (30% around 5 µm) and a relatively high transmission of 60% at 10.6 µm. SHG signals have been detected in these samples. Even if the optical results are not at the height of our expectation, the feasibility of this novel technique has been determinate and can be considered as a potential approach to synthesize novel glass-ceramic with specific properties.

Fig. 2 .

 2 Fig.2.

Fig. 1

 1 Fig.1

Fig. 4 .

 4 Fig.2 glass and


Zhuobin Li

Changgui Lin
email: linchanggui@nbu.edu.cn

Guoshun Qu

Laurent Calvez

Shixun Dai

Xianghua Zhang

Tiefeng Xu

Qiuhua Nie

Formation and properties of chalcogenide glasses based on GeS 2 -Sb 2 S 3 -AgI system

Keywords: Amorphous materials, Electrical properties, Optical materials and properties

Novel glasses in GeS 2 -Sb 2 S 3 -AgI system have been prepared by melt-quenching method. A large glass-forming region was found in the novel system, in which almost 60mol% AgI has been incorporated.

The basic physiochemical properties of glass samples were investigated. With the addition of AgI, red shift of short-wavelength absorption edge indicates and distinct drop of the glass transition temperature (T g ) were observed. In addition, a high Ag + ion conductivity of 6.37 10 -4 S/cm at room temperature can be obtained in 55(0.6GeS 2 -0.4Sb 2 S 3 )-45AgI sample, indicating that these glasses have potential application as amorphous solid electrolytes.

Introduction

For several decades, chalcogenide glasses have attracted much attention due to their interesting properties: excellent IR transmittance, low phonon energy, high nonlinear refractive index, and good glass-forming abilities. Therefore, these materials present great potential for infrared optics applications such as thermal imaging, laser power delivering, and ultrafast all optical switching [START_REF] Zhang | Production of complex chalcogenide glass optics by molding for thermal imaging[END_REF][START_REF] Zakery | Optical properties and applications of chalcogenide glasses: a review[END_REF][START_REF] Delaizir | Infrared glass-ceramics with fine porous surfaces for optical sensor applications[END_REF][START_REF] Abe | Preparation and properties of Ge-Ga-S glasses for laser hosts[END_REF][START_REF] Wang | Large and ultrafast third-order optical nonlinearity of GeS 2 -Ga 2 S 3 -CdS chalcogenide glass[END_REF]. Among numerous glasses, Ge-Sb-S has been well studied and has been shown to possess good thermal stability and high nonlinear optical properties. [START_REF] Takebe | Thermal stability and structure of Ge-Sb-S glasses[END_REF][START_REF] Fedus | Nonlinear characterization of GeS 2 -Sb 2 S 3 -CsI glass system[END_REF][START_REF] Petit | Correlation between physical, optical and structural properties of sulfide glasses in the system Ge-Sb-S[END_REF] Moreover, the large glass-forming region and the compositional dependencies of various properties make it possible to tailoring material for different applications. Previous research revealed that adding AgI into sulphide glass can greatly improve the nonlinear optical properties. [START_REF] Iliopoulos | GeS 2 -Ga 2 S 3 -AgI glasses with high nonlinear optical properties[END_REF] And the addition of haloid atom, iodine, would improve the glass-forming ability. In addition, superionic conducting chalcogenide glasses containing Ag ions have potential application in solid-state batteries. [START_REF] Kassem | New chalcogenide glasses in the CdTe-AgI-As 2 Te 3 system[END_REF][START_REF] Stehlik | Conductivity in Ag-As-S (Se, Te) chalcogenide glasses[END_REF][START_REF] Ureña | Ionic conductivity (Ag + ) in AgGeSe glasses[END_REF] Therefore, we choose GeS 2 -Sb 2 S 3 -AgI glasses which was not investigated before as research subjects.

In this paper, we synthesized chalcohalide glasses in GeS 2 -Sb 2 S 3 -AgI system and investigated their glass-forming ability, thermal, optical, and physicochemical properties.

Experimental

Homogeneous GeS 2 -Sb 2 S 3 -AgI glasses were obtained by melt-quenching method. High purity raw materials Ge, Sb, S (5N) and AgI (3N) were weighed in a glove box and mixed together. The mixtures were placed into pre-cleaned quartz ampoules and sealed under vacuum (~10 -3 Pa). Then, the ampoules were melted at 950 o C for 12h in a rocking furnace and quenched in ice water to obtain bulk glasses.

Subsequently, the glass samples were annealed at the temperature of T g -20 o C for 3h to remove inner constraints. Then the glass rods were cut and polished into disks of 10mm in diameter and 1mm in thickness.

Amorphous characteristics of the samples were confirmed by X-ray diffraction (Bruker D2 phaser, =0.15406 nm, 30 kv, 10 mA, CuK ). Densities were measured in de-ionized water based on the Archimedes principle. Vickers hardness values were obtained by Vickers microindenter (Everone MH-3, Everone Enterprises. Ltd., China) with a charge of 100g for 5s. The glass transition temperature (T g ) and the onset of crystallization temperature (T x ) were determined by DSC (TA Instruments Q2000, New Castle, DE) at a heating rate of 10 o C/min. The transmission spectra were recorded with a UV-Vis-NIR spectrophotometer (PerkinElmer Lambda 950, Waltham, MA) and FTIR spectrometer (Nicolet 381, USA).

In addition, the conductivities were calculated from impendence spectra which were carried out using an impedance analyzer (Agilent 4294A, USA). A relatively wide glass-forming region was determined in the case of quenching 10g melts in water and shown in Fig. 1. It can be seen that the glass forming region is very large, and AgI can be largely incorporated into the GeS 2 -Sb 2 S 3 glasses. In the pseudo-ternary system, the amount of dissolved AgI can be reach to ~55mol% when the ratio of GeS 2 to Sb 2 S 3 is 6/4 (series 1). With a constant of 10mol% GeS 2 content (series 2), the glass-forming region reaches to ~60mol% amount of AgI. The large glass forming region is important because the large amount of AgI can enhances ionic conductivity and provides super-ionic glasses. Fig. 2 shows the XRD patterns of some crystallized samples. Here the sample with the composition of xGeS 2 -ySb 2 S 3 -zAgI is named as x-y-z. It is obvious that no glass is obtained along the Sb 2 S 3 -AgI side. In the GeS 2 -AgI system, sample with 10% AgI has GeS 2 and -AgI crystalline separate out. In the pseudo-ternary system, along the series 1, sample with 60% AgI (24-16-60) has the separation of crystalline -AgI and -AgI. The detailed parameters of samples are provided in Table 1. It is obviously that, with increasing contents of AgI, the density increases and the hardness decreases. The evolution of density is easy to understand because of the heavy mass of AgI. The variation of hardness is also due to the addition of iodine atoms. As a non-bridging atom, iodine plays the role as the glass network terminator and breaks M-S-M (M=Ge or Sb) bonds to form M-I bonds. Thus, the addition of AgI decreases the dimensionality of structural network and makes the network more opened, and consequently resulting in the decrease of hardness. Previous research found that the T g have an intimate relationship with the crosslink density and the network connectivity of the glasses. [START_REF] Heo | Chalcohalide glasses: I. Synthesis and properties of Ge-S-Br and Ge-S-I glasses[END_REF] As discussed above, iodine atom is a glass network terminator, and the addition of iodine will induce the descending of network connectivity. Thus, the value of T g will decrease with the addition of AgI gradually. Fig. 3 shows the Vis-IR transmission spectra of GeS 2 -Sb 2 S 3 -AgI glasses. Most of these glasses have good transparency in IR region, but the transmission region becomes narrow with the addition of AgI.

Results and Discussion

According to previous researches [START_REF] Tao | Formation and properties of the GeS 2 -In 2 S 3 -KCl new chalcohalide glassy system[END_REF][START_REF] Yang | Glass formation and properties of GeSe 2 -Ga 2 Se 3 -MX (MX is alkali halide) chalcohalide glasses[END_REF], the addition of halides in chalcogenide glass would usually induce the blue shift of the cut-off edge of short wavelength ( vis ) due to the lower polarizability of haloid ions compared with S 2-ions. Herein, on the contrary, vis shifts toward the long wavelength with the addition of AgI. This is probably because of the high polarizability of Ag + ions. Furthermore, the absorption bands at 2.9 m, 6.3 m, and 7.7 m can be attributed to the -OH, H 2 O, and -S-O-, respectively.

These IR impurity absorption bands are enhanced with the addition of AgI because of its hygroscopic property.

As discussed above, the large amount of AgI may provide superionic glasses. To identify whether these glasses have superionic conducting characteristic, we employed impendence spectra to calculate the conductivity. The total conductivity contains ionic and electronic contribution. Here the electronic conductivity is negligibly small compared to the ionic one. The calculated results were plotted in Fig. 4.

The results showed that the conductivity at room temperature for 55(0.6GeS 2 -0.4Sb 2 S 3 )-45AgI is 6.37 10 -4 S/cm. The high conductivity can be attributed to the mobile Ag ions in glass matrix.

Conclusion

In this work, we prepared GeS 2 -Sb 2 S 3 -AgI chalcogenide glasses and determined the glass-forming region. Up to almost 60mol% AgI can be dissolved in this glass system. The glasses have excellent IR transmittance which makes them good materials for application in IR optics. In addition, the high Ag + ion conductivity of 6.37 10 -4 S/cm at room temperature can be obtained for 55(0.6GeS 2 -0.4Sb 2 S 3 )-45AgI sample. This results indicating that this glass system has a potential application in amorphous solid electrolytes.

Figure captions

  Fig.1 Fig. 2

  Fig.3 Fig. 4

Fig. 1

 1 Fig. 1 Glass-forming region of GeS 2 -Sb 2 S 3 -AgI system.

Fig. 2

 2 Fig.2XRD patterns of some crystallized samples and the JCPDF cards of no. 83-2157 -AgI and no.

Fig. 3 Fig. 4

 34 Fig.3Vis-IR transmission spectra of glass samples in series 1.

Table 1

 1 Density, hardness and characteristic temperature of the samples.

		Compositions	Density, ( 0.002g/cm 3 )	Hardness, H v ( 2kg/mm 2 )	T g ( 1 o C)	T x ( 1 o C)	T (T x -T g )
		90(0.6GeS 2 •0.4Sb 2 S 3 )-10AgI	3.749	160	231	399	168
		80(0.6GeS 2 •0.4Sb 2 S 3 )-20AgI	3.952	142	213	400	187
	Series 1	70(0.6GeS 2 •0.4Sb 2 S 3 )-30AgI	4.192	130	187	401	214
		60(0.6GeS 2 •0.4Sb 2 S 3 )-40AgI	4.441	114	182	402	220
		55(0.6GeS 2 •0.4Sb 2 S 3 )-45AgI	4.481	104	155	402	247
		10GeS 2 -80Sb 2 S 3 -10AgI	4.245	143	215	286	71
		10GeS 2 -70Sb 2 S 3 -20AgI	4.346	141	203	298	95
	Series 2	10GeS 2 -60Sb 2 S 3 -30AgI	4.397	136	187	305	118
		10GeS 2 -50Sb 2 S 3 -40AgI	4.616	120	178	305	127
		10GeS 2 -40Sb 2 S 3 -50AgI	4.762	107	162	313	151

Acknowledgements

This work was partially supported by the International Science & Technology Cooperation Program of China (Grant No. 2011DFA12040), 973 Program (Grant No. 2012CB722703), the NSFC (Grant No. 61108057), the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY14E020001), and State Key Laboratory of Silicate Materials for Architectures (Wuhan University of Technology) (Grant No. SYSJJ2013-03). It was also sponsored by K.C. Wong Magna Fund in Ningbo University.

2. The glass-forming region is very large in this system, and large amount of AgI can dissolved in this system.

3. The ionic conductivity at room temperature of 55(60GeS 2 -40Sb 2 S 3 )-45AgI can reach to 6.37 10 -4 S/cm, indicating that this glass system has a potential application in amorphous solid electrolytes.


Keywords: Phase measurement, Phase noise, Photodetectors, mode-locked lasers

It is shown that the results presented in the article by Wu et al. (IEEE Photon. Technol. Lett. 23 (n° 8) 2011, pp. 468-470), and attributed by the authors to amplitude-to-phase conversion in the photodetector, do not originate in the photodetector under test, due to the power dependence observed. More recent results show that conversion effects with the same size and frequency dependence are observed in passively mode-locked NPR (non-linear polarization rotation) mode-locked lasers.

n their article, K. Wu et al. [START_REF] Wu | Frequency response of the noise conversion from relative intensity noise in the photodetection of an optical pulse train[END_REF] address the problem of the amplitude-to-phase conversion in photodetectors, already observed in earlier publications. They present a particularly simple set-up, that may provide a convenient means to characterize the AM-to-PM conversion in high bandwidth photodetectors. They use a 2.4 mW free-running passively mode-locked laser at 147 MHz repetition rate, and modulate the power of the laser at audio frequencies by modulating the power of the pump diode. They subsequently detect the pulse train emitted by the mode-locked laser using a 2GHz photodiode. The signal of the photodiode is analyzed by a signal analyzer FSUP26, which can deliver -the relative intensity noise power spectrum and the phase noise of the 147 MHz signal, separately, (Fig. 2 a-and b-, respectively) as a function of the offset frequency -or the spectrum, in dBm of the signal around 147 MHz, Fig. 4.

Both figures show that the 147 MHz signal is phase-modulated at the frequency of the power modulation and at its harmonics. In Fig. 4, the phase modulation appears as a an asymmetry in the side bands: the asymmetry P ∆ is plotted in dB, in different conditions.

The important point is to confirm that the effect originates in the photodiode and not in the generation of the power-modulated pulse train. To confirm this, one can insert attenuators in front of the photodiode. As the mean power is reduced by a factor K, the amplitude of the power modulation is I also reduced by a factor of K, keeping the relative intensity noise (RIN) constant. Then one expects that the amplitude of the phase change will be accordingly reduced by a factor of K. In other words, one expects that the conversion ratio from RIN to phase noise is proportional to optical power. But data on fig. 3 show that when an attenuator is inserted the conversion ratio from RIN to phase noise is constant. The same observation can be made from Fig. 4: the ratio P ∆ , plotted in dB in Fig. 4-c, remains constant (less than 0.3 dB variation for a 6 dB variation of the RF power), whatever the attenuation of the optical power. The expected linearity is not observed.

It may seem naive to expect linearity with optical power in amplitude-to-phase conversion in photodetectors. With strong optical pulses a significant distortion occurs, as observed by Ivanov et al. [START_REF] Ivanov | Study of the excess noise associated with demodulation of ultra-short infrared pulses[END_REF] and others. But, as shown in [START_REF] Ivanov | Study of the excess noise associated with demodulation of ultra-short infrared pulses[END_REF], the non-linear behavior is essentially observed in high harmonics of the signal. For low frequency harmonics, no significant non-linearity is expected at a power of 2.4 mW or less. This is particularly well demonstrated in [START_REF] Wu | Characterization of the excess noise conversion from optical relative intensity noise in the photodetection of modelocked lasers for microwave signal synthesis[END_REF], where K. Wu et al. have varied the optical power at the photodiode using a variable optical attenuator and extensively studied the resulting temporal profiles of the pulses delivered by a 10 GHz photodiode. Non-linear features are specifically observed in high harmonics of the detected signal. With low harmonics of the signal, or more generally with harmonics at frequencies << 1 GHz, the RIN to phase noise conversion coefficient increases with optical power. This is particularly clear in Fig. 5-c (dotted line) corresponding to the fundamental frequency, where the RIN to phase noise conversion factor shows linear behavior. Same trend is observed in Fig. 5-b, and6, for frequencies << 1 GHz. Note that in the graphs of ref. [START_REF] Wu | Characterization of the excess noise conversion from optical relative intensity noise in the photodetection of modelocked lasers for microwave signal synthesis[END_REF] the horizontal axis does not start exactly at zero mW optical power.

For these reasons we believe that the absence of a dependence of the RIN-to-phase noise conversion factor on the optical power in [START_REF] Wu | Frequency response of the noise conversion from relative intensity noise in the photodetection of an optical pulse train[END_REF] raises suspicion that the observed phase noise may not be due to conversion in the photodetector.

As to the possible origin of the phase noise observed in [START_REF] Wu | Frequency response of the noise conversion from relative intensity noise in the photodetection of an optical pulse train[END_REF], ref.

[4] brings some more insight, by studying the pump-to-phase conversion in two different 1.5 µm passively mode-locked lasers in conditions where the authors can check that conversion in the photodetector is negligible. They measure the pump-to-phase noise conversion ratio in a NPR laser, and obtain the values listed in Table I. Not only these values are orders of magnitude above the estimate of 10 -9 obtained from the theoretical analysis mentioned in [START_REF] Wu | Frequency response of the noise conversion from relative intensity noise in the photodetection of an optical pulse train[END_REF], but they also match very well the values of the conversion ratio in [START_REF] Wu | Frequency response of the noise conversion from relative intensity noise in the photodetection of an optical pulse train[END_REF], Fig. 3, up to 30kHz.

We conclude that in ref. [START_REF] Wu | Frequency response of the noise conversion from relative intensity noise in the photodetection of an optical pulse train[END_REF], at least up to 30kHz offset frequency, the RIN-to-phase noise conversion in the laser dominates the observed phase noise just as in ref. [4]. More complete characterization, such as performed in ref. [START_REF] Wu | Characterization of the excess noise conversion from optical relative intensity noise in the photodetection of modelocked lasers for microwave signal synthesis[END_REF], is required before conclusively assigning the power-to-phase conversion observed in [START_REF] Wu | Frequency response of the noise conversion from relative intensity noise in the photodetection of an optical pulse train[END_REF] at 40 kHz and above to the laser or to the photodiode.

  Comment to "Frequency Response of the Noise Conversion From Relative Intensity Noise to Phase Noise in the Photodetection of an Optical Pulse Train", K. Wu et al, IEEE Photon. Technol. Lett. 23 (n° 8) 2011, p. 468 Duy-Ha Phung, Michel Lintz Laboratoire ARTEMIS, Univ. Nice Sophia, Observatoire de la Cote d'Azur and CNRS, Bd de l'Observatoire, 06300 Nice, France (e-mail: michel.lintz@oca.eu).

TABLE I PUMP

 I

	40	-16 / -17
	60	-22
		-TO-PHASE NOISE CONVERSION RATIO
	frequency	pump-to-phase noise
	(kHz)	conversion ratio (dB)
		(from [4], Fig. 2-a, blue
		curve)
	5	-3
	10	-7
	20	-9
	30	-14