B Recur
email: brecur@labri.fr

J P Guillet

I Manek-Hönninger

J C Delagnes

W Benharbone

P Desbarats

J P Domenger

L Canioni

P Mounaix
email: p.mounaix@loma.u-bordeaux1.fr

Propagation Beam Consideration for 3D THz Computed Tomography

Keywords:

In this paper, a model of the beam propagation is developed according to the physical properties of THz waves used in THz computed tomography (CT) scan imaging. This model is first included in an acquisition simulator to observe and estimate the impact of the Gaussian beam intensity profile on the projection sets. Second, the model is introduced in several inversion methods as a convolution filter to perform efficient tomographic reconstructions of simulated and real acquired objects. Results obtained with three reconstruction methods (BFP, SART and OSEM) are compared to the techniques proposed in this paper. We focus our discussion on the efficiency of optimized algorithms to increase the overall quality and accuracy of the reconstructions.

Introduction

Terahertz (THz) technology, and especially THz spectro-imaging, is now a well-established tool in the field of contact-free and non-destructive testing (NDT). While commercial devices become available, the fundamental issues of the imaging process [START_REF] Ferguson | T-ray computed tomography[END_REF] often remain overlooked. In the field of 3D imaging, X-Ray Computed Tomography (CT) is an omnipresent technique which provides cross-sectional images of an object by analyzing the radiation transmitted by the sample through different incidence angles. This technique provides 3D visualization of dense materials such as human body, biological tissues and also starts to enter in the industrial field. Nevertheless, this powerful technique cannot be easily applied to soft materials such as plastics, papers or paintings owing to the low absorption of the X-Ray radiation for example. Alternatively, THz radiation proposes attractive features such as non-invasive and non-destructive analysis, transparency and good penetration depth through various materials specially below 1 THz. All these remarkable properties make THz radiation very efficient for direct applications in non-destructive inspection and the security field. Most of the experimental demonstrations were performed in 2D whereas THz CT, which is a powerful technique, the literature remains scattered [START_REF] Ferguson | T-ray computed tomography[END_REF][START_REF] Wang | T-ray imaging and tomography[END_REF][START_REF] Wang | Pulsed terahertz tomography[END_REF][START_REF] Awad | Transmission terahertz waveguide-based imaging below the diffraction limit[END_REF][START_REF] Yin | Wavelet based local tomographic image using terahertz techniques[END_REF][START_REF] Brahm | Volumetric spectral analysis of materials using terahertz-tomography techniques[END_REF].

The first reason concerns the diffraction effects and Fresnel losses experienced by the propagation of the THz wave through the sample [START_REF] Abraham | Refraction losses in terahertz computed tomography[END_REF]. Secondly, although low NEP (Noise Equivalent Power < 10 -9 W/Hz 1 2 at room temperature) -and consequently fast detectors [START_REF] Nadar | Room temperature imaging at 1[END_REF] -have been developed and successfully applied in imaging [START_REF] Fatimy | Plasma wave field effect transistors as a resonant detector for imaging applications up to one terahertz for terahertz imaging[END_REF], they are not yet integrated in an array configuration. Detectors are thus mono-to few-pixels large, resulting in a long scanning process in order to acquire 2D images. Reconstruction algorithms allowing accurate reconstruction from a limited number of slices are crucial in order to circumvent these current technical limitations, but also for future development. The limitation is also directly connected to the number of projection data. At least, an important consideration in CT concerns the choice of the reconstruction method to be able to visualize the different cross-sectional images and the final 3D volume of the sample. In X-Ray, iterative reconstruction methods have been proposed for X-Ray CT such as the Simultaneous Algebraic Reconstruction Technique (SART) [START_REF] Andersen | Simultaneous algebraic reconstruction technique (SART) : A superior implementation of the ART algorithm[END_REF] and the Ordered Subsets Expectation Maximization (OSEM) [START_REF] Shepp | Maximum likelihood reconstruction for emission tomography[END_REF][START_REF] Hudson | Accelerated image reconstruction using ordered subsets of projection data[END_REF]. These well-established techniques inherited from X-Ray know-how were successfully applied in a first approximation to THz CT.

In this paper, we propose to improve the physical modeling by adding an heuristic propagation of a gaussian beam. We aim to take into account a more realistic physical behavior of the electromagnetic waves used in THz CT. This approach is justified by the fact that the reconstruction methods assume a ray tracing approach while THz beam profile is very far from this basic hypothesis. There is indeed a trade-off range in the focusing condition of the diffracting THz wave. While 2λ -waist beams can be qualitatively treated as a ray of light, tightly focused ones (down the ultimate resolution of λ /2) can badly accommodate with the ray tracing approach of all the reconstruction methods used in X-Ray. This model is first included in an acquisition simulator to observe and estimate the impact of the gaussian beam distribution on the acquisition images. Second, the model is tested in several reconstruction methods as a convolution/deconvolution filter to perform a more efficient tomographic reconstruction of simulated and real acquired objects. Results obtained with three usual methods (BFP, SART and OSEM) are compared to the new methods proposed in the paper. The discussion focuses on the efficiency of optimized algorithms to increases the overall quality and accuracy of the reconstructions.

THz Computed Tomography

Experimental Setup Properties

The experimental setup of the 3D millimeter wave tomographic scanner is shown in Fig. 1(a). The output beam of a compact millimeter wave (mmw) Gunn diode coupled with a horn antenna is collimated using an off-axis parabolic mirror. The Gunn diode used is a 80 GHz diode coupled to a frequency tripler delivering 0.3 mW at 240 GHz (wavelength 1.25 mm). The THz beam is then focused with a Teflon lens on the sample which is positioned on a three-axes motorized stage comprising the X,Y and θ movements, respectively. Fig. 1(b) shows the 2D transversal profile of the THz beam at the beam waist visualized using a photothermal THz convertor. This result shows that, at the sample position, the beam profile is homogeneous with a Gaussian circular shape (2 mm beam diameter, measured at FWHM) in agreement with the theoretical values obtained from the propagation of Gaussian beam models. This result indicates that the spatial resolution of the 3D millimeter wave tomographic scanner is limited to a few millimeters owing to the long wavelength of the emitting sources. Consequently, the system is more adapted for the visualization of sub-centimeter structures within large size object, typically more than (100 × 100 × 100) mm 3 . In order to perform a 3D reconstruction of volumetric objects, the experimental procedure is organized as follows [START_REF] Younus | 3D millimeter wave tomographic scanner for large size opaque object inspection with different refractive index contrasts[END_REF]. First, we record a 2D transmission image of the sample by moving the object in the X and Y directions with a scan rate of 10 Hz. Usually a (1 × 1) mm 2 scan step is selected. The acquisition time for a (100 × 100)mm 2 image size is about 15 minutes. Then, the sample is rotated by a rotation step dθ in order to provide a different visualization of the object. The operation is repeated N θ times from θ = 0 • to θ = 180 • and we finally get a set of N θ projections of the sample corresponding to the different angles of visualization. For instance, if N θ = 18 and dθ = 10 • , the total acquisition time is about 5 hours for the complete 3D visualization of the sample. However, to visualize only a single cross-sectional image of the sample, corresponding to a 100 mm horizontal scan associated to 18 different projections, this acquisition time is reduced to approximately 3 minutes. From these projection data, we are able to construct the sinogram of the object which represents, for a given horizontal slice, the evolution of the transmitted THz intensity as a function of the rotation angle. Finally, we apply tomographic algorithms to reconstruct the final 3D volume of the sample.

Usual Tomographic Reconstruction methods

Tomography is used to reconstruct the volume of an object from the set of projections performed on the exterior of the object [START_REF] Herman | Image Reconstruction From Projections : The Fundamentals of Computerized Tomography[END_REF][START_REF] Toft | The Radon Transform : Theory and Implementation[END_REF]. This technique, widely developed in X-Ray CT scan imaging, is modeled by the Radon theorem [START_REF] Radon | Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten[END_REF]. The direct transform R describes the projection line acquisition. It maps a 2D function defined by f (x, y) into a 1D projection along an angle θ and a module ρ. It is defined by the following formula : The reconstruction process is given by the inverse Radon transform which recovers the original domain from the projections. Given a sinogram S h (θ , ρ) containing several R θ (ρ) values at the cross-section depth h, the discrete inverse Radon transform computes each image pixel as follows :

R θ (ρ) = ∞ -∞ ∞ -∞ f (x, y)δ (ρ -x cos θ -y sin θ )dxdy (1)
I(i, j) = N θ -1 ∑ i θ =0 Nρ 2 ∑ ρ=- Nρ 2 W θ (i θ ) (ρ)A (θ ,ρ),(i, j) (2)
where :

• θ (i θ ) = i θ π N θ ,
• A (θ ,ρ),(i, j) is the weight-matrix defining the weight value between each pixel and each projection line,

• W θ (ρ) = Nρ 2 ∑ ν=-Nρ 2 |ν|   Nρ 2 ∑ ρ s =-Nρ 2 R θ (ρ s )exp (-i2πρ s ν)   exp (i2πρν).
First, this inversion filters each projection R θ in the Fourier domain with the ramp filter |ν| to increase geometric details. Second, it computes the pixel values from the filtered projections W θ (i θ ) . This method, denoted back-projection of filtered projections (BFP), is widely used in THz CT imaging since it is proposed in most of CT software tools. However, it is known that BFP suffers from several drawbacks such as the beam hardening and noise sensitivity.

To overcome these problems, the iterative methods SART (Simultaneous Algebraic Reconstruction Technique) [START_REF] Andersen | Simultaneous algebraic reconstruction technique (SART) : A superior implementation of the ART algorithm[END_REF] and OSEM (Ordered Subset Expectation Maximization) [START_REF] Hudson | Accelerated image reconstruction using ordered subsets of projection data[END_REF] have been introduced for THz CT imaging in [START_REF] Recur | Investigation on reconstruction methods applied to 3D terahertz computed tomography[END_REF]. The SART method is based on the Karczmarz algorithm used to approach the solution of the linear equation system I = A T R, where I is the image, R is the sinogram and A is the weight-matrix [START_REF] Gordon | Algebraic Reconstruction Techniques (ART) for Three-dimensional Electron Microscopy and X-ray Photography[END_REF]. SART is an iterative process follow-

ing k ∈ [0 • • • N iter [. Each sub-iteration s, 0 ≤ s < N θ ,
updates each pixel of the image I k,s by comparing the original projection R θ s with R k θ s (computed from I k,s-1 ) as follows :

I k,s (i, j) = I k,s-1 (i, j) + λ N ρ -1 ∑ i ρ =0 A (θ ,ρ),(i, j) R θ s (ρ) -R k θ s (ρ) D θ s (ρ) N ρ -1 ∑ i ρ =0 A (θ ,ρ),(i, j) (3)
where :

• D θ (ρ) = W -1 ∑ i=0 H-1 ∑ j=0 A (θ ,ρ),(i, j) is the norm of the segment (θ , ρ) crossing the image, • R k θ s (ρ) = W -1 ∑ i=0 H-1 ∑ j=0 A (θ s ,ρ),(i, j) I k,s-1 (i, j), • (W × H) is the image size.
A super-iteration k is completed when all the projections have been used. Iterations in k are performed until the convergence of the solution. The initial I 0,0 image is usually an uniform image.

The OSEM algorithm [START_REF] Shepp | Maximum likelihood reconstruction for emission tomography[END_REF] is another iterative process which slightly differs from the SART. The update is done from a subset of several projections at once and the error correction is multiplicative :

I k+1 (i, j) = I(i, j) k N θ -1 ∑ i θ =0 N ρ -1 ∑ i ρ =0 A (θ ,ρ),(i, j) R θ (ρ) R k θ (ρ) N θ -1 ∑ i θ =0 N ρ -1 ∑ i ρ =0 A (θ ,ρ),(i, j) (4)
The scheme on Fig. 3 summarizes the iterative method process. The images on Fig. 2(c-e) represent the reconstructions from the sinogram on Fig. 2(b) using the three methods. In our example, these results reveal a part of a tablet inside the medicine box.

From Propagation Beam Modeling to Tomographic Reconstruction Optimizations

Propagation beam observation and Modeling

In X-ray CT transmission processes, the beam shape can be considered constant because of the smallness of the wavelength with respect to the object size so that there is no diffraction. For the same reason, the intensity distribution is uniform over the beam cross-section. This property allows Radon model to be used directly in all reconstruction methods.

In THz CT imaging, the propagation beam is close to a Gaussian distribution which is both determined by the THz wave properties and, eventually, the lens used to enforce the beam focus. The radius of the beam (from the beam axis) has its minimum value w 0 at the so-called beam waist. According to the wavelength λ , the radius at the position z from the beam waist is :

w(z) = w 0 1 + z z R 2 ( 5
)
where z R = πw 2 0 λ is the Rayleigh range. Moreover, the intensity distribution over the crosssection is given by :

I(r, z) = I 0 w 0 w(z) 2 exp -2r 2 w 2 (z) (6)
where :

• r is the distance from the beam axis,

• I 0 is the intensity at the center of the beam waist.

As an illustration, Fig. 4(a) shows beam cross-sections observed for a 240 GHz source along the Z-axis with a 5mm step. Note that the energy decreases from the center to the edge of the beam following a Gaussian distribution. A profile at the central plane of the beam is given in Fig. 4(b). It shows the variation of the radius (horizontally) and the Gaussian distribution of the intensity (vertically). Knowing the source properties and using the Eq. ( 5) and Eq. ( 6), the observed Gaussian beam can be computed to simulate a given source. For instance, Fig. 5 shows the 3D profile and energy distribution of a beam simulating the 240 GHz source. When the beam is focalized by a lens, THz source is modified by the influence of the lens which as well is treated by a Gaussian model. In such a case, the overall Gaussian beam is expressed as a convolution of both beams modeling the source and the lens. If the propagation beam distribution is unknown, the overall model could be estimated from each observation of the intensity profiles given in Fig. 4(a) using, for example, a non trivial 3D Newton-Gauss algorithm.

Simulated Acquisition

Using the Gaussian beam modeling, we develop now the simulated acquisition from such a beam. Fig. 6 illustrates the θ -projection acquisition. An object is modeled in a N 2 pixel image and the Gaussian beam is given at the same size and resolution. The object is rotated by θ from the original angular position to perform easily the column-by-column convolutions with the Gaussian beam. These convolutions simulate at each depth of the projection point of view (POV), the manner that the beam acquires the object. Then, they lead to a modified object corresponding to what it is viewed by the sensors. Finally, the acquisition of N samples leads to the projection acquired through the Gaussian beam. The process is easy to extend in 3D : each 1D convolution is replaced by a 2D convolution between each depth-image and the corresponding 2D cross-section of the beam. Mathematically, this process is obtained by the following optimized version of the Eq. ( 1) :

R φ =0 (ρ) = ∞ -∞ f θ (x, y = ρ) * I(x -x 0 , ρ -y 0 )δ (ρ -x cos φ )dx ( 7
)
where I(x, y) is the Gaussian propagation model ( 6), * is the convolution operator and (x 0 , y 0 ) is the center of the beam waist. The f (x, y) domain is rotated by θ to assume φ = 0. It leads to an horizontal acquisition allowing an easier computation of the column-by-column convolutions. Note that the integral along y is simplified by fixing the value y = ρ.

As an illustration, let us consider the image Fig. 7(b) representing the four metallic bars of the object in Fig. 7(a). An usual Radon acquisition is shown in Fig. 8(a). Simulated acquisition using Gaussian beam convolutions is given in Fig. 8(b). In such an acquisition, the edges are not well defined anymore. Then, the simulated sinogram characteristics are closer to the real acquisition given in Fig. 8(c). It puts in evidence the better reliability of our model to simulate the THz physical acquisition phenomenon and moreover, the discrepancy between Gaussian beam and ray-tracing approaches.

Tomographic Reconstruction Optimizations

Up to here, the modeling and the influence of the Gaussian beam have been introduced. Now, we deal with its consideration in the reconstruction methods in order to try to reduce induced artifacts.

Using the BFP, the idea consists in inverting the convolution proposed in Fig. 5. The projection acquired through a Gaussian beam, denoted R E θ , is retroprojected into a temporary image

I E φ =0 sized N 2 .
The image is deconvolued column-by-column with the beam model to obtain I θ . This one is rotated by the angle -θ and added to the result image. The Wiener deconvolution method [START_REF] Dhawan | Image restoration by Wiener deconvolution in limited-view computed tomography[END_REF] is used to avoid well-known problems of direct deconvolution in Fourier space. Using iterative methods, the projection acquired through the Gaussian beam at an iteration k is given by the discrete version of the Eq. ( 7). The update step comparison between computed and measured acquisitions becomes consistent because the projections are both obtained through a simulated/real Gaussian beam. Moreover, similarly than BFP, the obtained error projection is deconvolued before it is added in the I k+1 image. Everything else in the algorithm Fig. 3 remains the same.

Results and Discussion

Discussion from simulated acquisition

Images in Fig. 9(a-c) correspond to the results obtained with BFP, SART and OSEM from the theoretical sinogram Fig. 8(a). Fig. 9(d-f) represent the images obtained with the usual methods from the simulated sinogram Fig. 8(b). The distortions of each metallic bar circular shape are a consequence of the Gaussian distribution encountered during the acquisition. Inversely, images on Fig. 9(g-i), which are obtained from the simulated acquisition using the optimized methods, provide a closer circular shape of the metallic bars.

To show the new method efficiency, quality and accuracy of the results are now compared to each other using image-based comparison metrics. First, the quality preservation is estimated using the equivalence rate between two images. The image properties are compared to each other using the Structural SIMilarity (SSIM) criterion [START_REF] Wang | Image quality assessment : From error visibility to structural similarity[END_REF] :

SSIM(I, J) = l(I, J) • c(I, J) • r(I, J) (8)
where 0 ≤ l(I, J) ≤ 1 (resp. 0 ≤ c(I, J) ≤ 1) is the global intensity (resp. contrast) comparison between two images I and J, and 0 ≤ r(I, J) ≤ 1 is the correlation coefficient. 0 ≤ SSIM(I, J) ≤ 1 gives the quality rate of J compared to the reference I. The closer the SSIM value is to 1, the better the reconstruction quality is. Table 1 gives quality results for each image on Fig. 9 according to the theoretical signal Fig. 7(b) chosen as reference. Quality results from the images Fig. 9(a-c) show that iterative reconstructions are better than BFP, especially the OSEM method. Results from images Fig. 9(df) highlight the quality loss induced by the Gaussian beam acquisition : SSIM decreases at least by 6%. The detail of SSIM metrics shows that the geometrical properties of the reconstructed images are degraded. The optimized techniques proposed in this paper allow a better recon-struction of the geometry whatever the method. For instance, r increases by 5% with OSEM, and SSIM is globally more accurate with optimized BFP and OSEM. However, it generates luminance and contrast losses with the SART method.

(a) (b) (c) (d) (e) (f) (g) (h) (i)
To complete the quality analysis, an accuracy study is proposed by a comparison of the horizontal profiles of the top bar. Profiles given by the BFP, SART and OSEM reconstructions are shown in Fig. 10(a-c). Whatever the method, the theoretical profile (red curves) is not well recovered even if it is reconstructed from a theoretical sinogram (green curves). However, it is close to the great profile whereas reconstructions from Gaussian beam simulation lead to a spreading of the profile (blue and violet curves). Using the optimized techniques, the spreading is significantly reduced (violet curves), especially using the optimized SART. Fig. 10(d) compares the profiles obtained by the optimized techniques and the theoretical signal. These results confirm that the optimized SART gives the minimal spreading, followed by the OSEM and finally by the BFP technique. Then, for a given acquisition, SART provides a better accuracy than BFP and OSEM.

2D and 3D reconstructions from real acquisitions

Reconstructions computed from the real acquisition Fig. 8(c) are proposed in Fig. 11. The lesser spreading of the metallic bars observed with the optimized methods confirm the theoretical analysis results discussed above. Images given in Fig. 12 show 3D reconstructions of the medicine box. These visualizations are obtained from the stacks of reconstructed cross-sections, computed one-by-one from the 3D acquisition (stack of sinograms). Using the standard methods, each cross-sectional image is directly computed from its corresponding sinogram. Inversely, the optimized methods need all the sinograms at once to take into account the 3D propagation beam model. From the results, we can remark a better quality and accuracy of details in general. For example, the contact area (defined by the high-intensity pixels) between the tablet and the box is easier to estimate. Indeed, as we can see in the cross-sectional images in Fig 13, this area is less thick on the results obtained with optimized methods. Such qualitative analysis improvement highlights the need to take into account the propagation beam into the tomographic reconstructions for THz CT.

Conclusion

We demonstrated a development of an improved beam propagation model taking into account the physical properties of THz waves used in THz computed tomography (CT) scan imaging. This more realistic model is clearly justified by the fact that previous models were simply relying on well-known and commonly applied X-Ray reconstruction methods, which assume a ray tracing approach, whereas the THz beam profile is very far from this basic hypothesis. Therefore, we included in an acquisition simulator the Gaussian beam intensity profile in order to observe and to estimate its impact on the projection sets. The simulated sinogram characteristics are found closer to the real acquisition and demonstrate the better reliability of our model to simulate the THz physical acquisition process. Moreover, the discrepancy between Gaussian beam and ray-tracing approaches has been studied. At least, the model is introduced in several inversion methods as a convolution filter to perform efficient tomographic reconstructions of simulated and real acquired objects. Results obtained with three different reconstruction methods (BFP, SART and OSEM) have been compared on the basis of the efficiency of optimized algorithms to increase the overall quality and accuracy of the reconstructions. This rigorous quantitative approach provides a new insight for the improvement of 3D THz CT imaging.

Fig. 1 .

 1 Fig. 1. (a) Experimental setup. L1 -L2 : HDPE lenses, PM1 -PM2 : Parabolic Mirrors. (b) 2D spatial profile of the THz beam waist at the sample position (240 GHz source) visualized with a pyroelectric detector.

Fig. 2 .

 2 Fig. 2. (a) Medicine box acquired at the indicated cross-section. (b) Corresponding sinogram with N θ = 18 and N ρ = 46. (c) BFP, (d) SART, (e) OSEM results.

Fig. 3 .

 3 Fig. 3. Iterative reconstruction process.

Fig. 4 .

 4 Fig. 4. (a) Propagation beam acquired along the Z-axis with a 5 mm step. (b) Beam propagation along the Z-axis.

Fig. 5 .

 5 Fig. 5. Simulated propagation of the beam for a 240 GHz source (Intensity (a.u), position in meters).

Fig. 6 .

 6 Fig. 6. Simulated acquisition of a projection θ in 2D.

Fig. 7 .Fig. 8 .

 78 Fig. 7. (a) Object composed of four metallic bars (two bars diameter 10mm on the top and on the left, one bar diameter 12mm on the right and one bar diameter 8mm on the bottom), (b) Synthetic model of the object.

Fig. 9 .

 9 Fig. 9. (a)(b)(c) BFP, SART, OSEM results from the ideal sinogram Fig. 8(a). (d)(e)(f), BFP, SART, OSEM from simulated Gaussian beam acquisition 8(b). (g)(h)(i) BFP, SART and OSEM reconstructions from the same sinogram using optimized algorithms.

Fig. 10 .

 10 Fig. 10. Top bar profiles reconstructed with BFP (a), SART (b) and OSEM (c) : from the theoretical sinogram (Green) and from the simulated Gaussian acquisition with usual (blue) and optimized (Violet) methods. (d) : Top bar profiles reconstructed with the optimized methods. (Green) : BFP. (Blue) : SART. (Violet) : OSEM. (Red) : Theorical signal.

Fig. 11 .

 11 Fig. 11. (a)(b)(c) Usual BFP, SART and OSEM results from the real acquisition Fig. 8(d). (d)(e)(f) Optimized BFP, SART and OSEM results.

Fig. 12 .Fig. 13 .

 1213 Fig. 12. 3D reconstructions of the medicine box using usual BFP (a), SART (b) and OSEM (c) compared to the optimized BFP (d), SART (e) and OSEM (f) methods.

Table 1 .

 1 Comparison between reconstruction from sinogram acquired through a Gaussian beam and the original domain. It relates on the quality rate of each method to reconstruct the original image.

	Image	l	c	r	SSIM
	(a)	0.99 0.98 0.99	0.96
	(d)	1.00 0.97 0.93	0.90
	(g)	0.99 0.97 0.95	0.92
	(b)	0.99 0.99 0.98	0.97
	(e)	1.00 0.97 0.94	0.91
	(h)	0.97 0.94 0.95	0.87
	(c)	1.00 1.00 1.00	0.99
	(f)	1.00 0.97 0.93	0.91
	(i)	0.99 0.98 0.98	0.94


Jan E M Houben

Grammar & Other Modes of the Mind

1. According to an oft-quoted line of Rudyard Kipling, "East is East and West is West, and never the twain shall meet." In the person of Professor Ashok Aklujkar, however, East and West do meet and that too in a fortunate and fruitful way. As a specialist of Sanskrit grammar, specifically Pāṇinian grammar, and of the philosophy of Sanskrit grammar, specifically the philosophy of Bharthari, he maintains a keen interest in modern "Western" philosophy and has been an admirer of W.V.O. Quine ever since his time at Harvard University.

However, in spite of important similarities and of numerous borrowings from ancient Indian linguistics into western linguistics since the nineteenth century, it can be said that in the domain of grammar "East" is, to a large extent, still "East" and "West" still "West." A point where the Indian grammatical tradition differs significantly and perhaps fundamentally from modern western linguistics is the following: Indian grammar and the theoretical reflections associated with it since Patañjali (2 nd cent. B.C.E.) have a considerable overlap and occasionally a tensed relationship with what from a western perspective are entirely different domains such as philosophy, religion and prayer.

Why should there be any competition or any tensionpresupposing an overlap -between on the one hand grammar and on the other hand philosophy, religion and prayer? Still, that is what we find in the tradition of Sanskrit grammar. To honour Professor Ashok Aklujkar who in his teaching and in his publications has contributed to all the domains involved in this question -grammar, philosophy and religion -I would here like to briefly explore some of its aspects.

2.1 Since grammar occupied such an important position among the sciences, we find references to its importance and discussions about its usefulness or otherwise in works and traditions outside grammar. In a famous line of a song attributed to Śaṅkara the study of grammar is said to be of no value (from a religious point of view) at the moment of dying. Hence instead of studying grammar one should adore the Lord: bhaja govindam (3x) ... mūḍhamate / saṁprāpte saṁnihite kāle na hi na hi rakṣati 'ḍuk ñ karaṇe' // This may be rendered as: "Adore the Lord ... o fool! When the appointed time (for departure from this life) comes, (a grammatical rule such as) ḍukñ karaṇe will, indeed, in no way save you." 1 Apparently the reference is to a student of grammar who tries to learn the Dhātupāṭha by heart.

The problem perceived was perhaps similar but the solution proposed quite different in the grammars of Rūpagosvāmin and Jīvagosvāmin. In his Systems of Sanskrit Grammar, Belvalkar has the following to say about these grammars (1915: 94-95): 95. Later sectarian schools. -We now come to a class of grammmarians who have carried to extremes the tendency, already present, as we saw, in Bopadeva, to make grammar the vehicle of religion: and prominent amongst these are the Vaishnava grammars called Harināmāmta. 96. Harināmāmta. -There are two works going by this name. The one by Rūpagoswāmin, the companion and disciple of Chaitanya (1484-1527) and the author of several other Vaiṣṇava works, is perhaps the older of the two. The peculiarity of this work is the employment of various names of Kṣṇa and Rādhā, and of their acts, not simply by way of illustration but as actual technical terms. Thus the vowels of the pratyāhāra ac are each designated by the different incarnations of Viṣṇu ... 1 Mahadevan 1980: 37-38. ḍuk ñ is the form in which the root k is read in the Dhātupāṭha (VIII.10 ḌUk Ñ karaṇe), as it is provided with two anubandhas which indicate its grammatical properties: ḌU which indicates that the root forms an adjective ending in -trima (A 3.3.88) and Ñ indicating that ātmanepada forms derived from this root signify that the fruit of the action is intended for the agent (A 1.3.72). karaṇe indicates the domain of meaning associated with the root "in the meaning domain of 'doing'."

As is to be expected, beyond the introduction of this sectarian element no other improvement on the existing texts of grammar is here to be met with. The whole subject is presented to us in a dull uninteresting manner.

The Harināmāmta grammar of Jīvagosvāmin, nephew and follower of Rūpagosvāmin, contains the following opening verses:

vyākaraṇe maru-nīvti -jīvana-lubdhāḥ sadāgha-saṁvighnāḥ / hari-nāmāmtam etat pibantu śatadhāvagāhantām // 3 // "sāṅketyaṁ pārihāsyaṁ vā stobhaṁ helanam eva vā / vaikuṇṭha-nāma-grahaṇam aśeṣāgha-haraṁ viduḥ" // 4 //

The first verse may be rendered as: "Those eager for life in the desert area of grammar, always having mistakes and obstacles, let them drink this nectar of the names of Hari, a hundred times let them dive into it." The second verse, actually a quotation from the Bhāgavata-Purāṇa (6.2.14), means "Wether it be conventionally, to laugh, as praise or as joke, it is known that to pronounce the name of Vaikuṇṭha (Viṣṇu) takes away all impureties." Belvalkar's negative judgement is not entirely fair as there is a complex and instructive iconicity: the relationships between figures in Kṣṇa's and Vaiṣṇava mythology carefully mirror relationships between elements in the grammar. Moreover, the grammar contains "updates" to Pāṇini's grammar, for instance when it prescribes the respectful use of the second person plural for a single person or for two (HA 4.2, yuṣmado gaurave tv ekatve dvitve bahu-vacanam).

2.2 It is well-known that an early exponent of Kashmirian Śaiva Advaita, Somānanda, severely criticized Bharthari for straying away from his main task as grammarian -to explain the form of words -and for starting to deal with a field that is not his own: the search for knowledge that leads to liberation. 2 Somānanda's successors, however, Utpaladeva and Abhinavagupta, show great respect to Bharthari and refer to his philosophy to support their own position. 3 3.1 Turning now to mainstream grammatical thought, we find references to unexpected dimensions of grammar and grammatical language as early as in Patañjali's Mahābhāṣya on the grammar of Pāṇini. In an expression which seems to make little sense from a strictly grammatical or linguistic point of view, it is said (MBh III:58.14-15): ekaḥ śabdaḥ saṁyag jñātaḥ śāstrānvitaḥ suprayuktaḥ svarge loke kāmadhug bhavati-iti. "A single word, correctly known, conforming to the science (of grammar) and correctly employed becomes wish-fulfilling in heaven." From the nature of the preceding discussion 4 and from the use of iti at the end we can infer that the statement is a citation; the source, however, is not known.

The same statement, with the sequence of śāstrānvitaḥ and suprayuktaḥ inverted, is found in Bharthari's MBhD I:11.1-2, where it is introduced with asti hi smtiḥ "for there is a traditional text." Bharthari refers here to this statement to show that there is indeed traditional support in the form of a smti text for the stanza which the Mahābhāṣya gives to express one of the purposes of grammar (MBh I:2.19-20), yas tu prayuṅkte kuśalo viśeṣe śabdān yathāvad vyavahārakāle / so 'nantam āpnoti jayaṁ paratra vāgyogavid duṣyati cāpaśabdaiḥ But he who is skilful and uses words with regard to a 3 [START_REF] Torella | The Īśvarapratyabhijñ ākārikā of Utpaladeva with the Author's Vtti: critical edition and annotated translation[END_REF][START_REF] Torella | The Īśvarapratyabhijñ ākārikā of Utpaladeva with the Author's Vtti: critical edition and annotated translation[END_REF]Torella , 2009. 4 . 4 The preceding discussion culminates in the statement that it has been said (ukta) that there is indeed a purpose in the knowledge and in the employment of a word. It is next asked kim? which must either mean "which (purpose)" or "how (is it expressed)." To this question ekaḥ śabdaḥ … iti is supposed to be a reply. A few lines before this passage, a similar pattern is found of a general statement (that there is a purpose in ijyā 'ritual worship') followed by the question kim and next a citation from an unknown source (on the reward that is there svarge loke for someone following the ritual prescription to perform the Agniṣṭoma). particular topic appropriately at the time of communication, he obtains unending victory in the world beyond as he knows the method (yoga) of speech; through substandard words, however, he goes down.

Kaiyaṭa in his commentary on the Mahābhāṣya shows familiarity with Bharthari's Mahābhā ṣya-Dīpikā where we can verify this. In the same context of the Mahābhāṣya discussion of the stanza yas tu prayuṅkte … Kaiyaṭa first of all informs that this is part of a set of stanzas composed by Kātyāyana (MBh (b) p. 28). Next he says there is a text in support of this stanza composed by Kātyāyana which is not just a smti 'traditional text' but even a śruti 'revealed text': asya ślokasya śrutir anugrāhikāsti, after which Kaiyaṭa cites ekaḥ śabdaḥ … 5

The statement ekaḥ śabdaḥ … (which the Mahābhāṣya does not mention here but at a much later occasion) refers to two requirements with regard to a word, (a) a proper knowledge in accordance with the teachings of grammar; (b) a proper employment of the word in speech. The fulfilment of these two as it seems quite worldly requirements is supposed to lead to a remarkable, apparently otherworldly result, a wishfulfilling "cow" in heaven. In the stanza yas tu prayuṅkte … the emphasis is even more strongly on the appropriate employment of the words. The proper understanding of the word in accordance with grammar is not referred to but it may be taken to be implied in kuśala "skilful"6 and it is again evoked in vāg-yoga-vid "knowing the method of speech." The yoga in this compound, an 5

The citation appears here in the form ekaḥ śabdaḥ sujñātaḥ suṣṭhu prayuktaḥ svarge loke kāmadhug bhavati. The form which it has in MBh III:58.14-15 and the one in the MBhD I:11.1-2 seem more correct and in any case both these forms show a structure of three times eight syllables (if svarge is restored to s u varge) followed by bhavati. It remains to be investigated how widespread the tendency to octosyllabic formulation in early sanskrit prose, demonstrated for the Pūrva-mīmāṁsā-sūtra and for grammar (e.g. H. [START_REF] Smith | Retractiones Rhythmicae[END_REF]Smith , 1953;;H. Scharfe 1977: 92 note 25), really was. action noun derived from the root yuj, apparently refers to the knowledgeable employment of words; it evokes two other words with forms from the root yuj: suprayuktaḥ of the ekaḥ śabdaḥ … statement and prayuṅkte in the stanza yas tu prayuṅkte … In both cases yuj apparently implies the employment (prayoga) of speech in communication. In the same section on purposes of grammar in the introductory chapter (Paspaśā) of the Mahābhāṣya we also find the root yuj employed with regard to the employment of speech in ritual.

3.2 A different use of a derivative of yuj with regard to speech or the word (śabda) is found in the Vākyapadīya, VP 1.143-144.

api prayoktur ātmānaṁ śabdam antar avasthitam / prāhur mahāntam ṣabhaṁ yena sāyujyam iṣyate // tasmād yaḥ śabdasaṁskāraḥ sā siddhiḥ paramātmanaḥ / tasya pravttitattvajñas tad brahmāmtam aśnute // They even say that the word situated within is the ātman 'Self' of the speaker, the Great Bull with whom one desires to be in union (sāyujyam). That is why this perfection of words (following grammar) -it is the realisation of the supreme Self. He who knows the principle of the procedures of this (grammatical perfection) achieves the immortal Brahman. This passage goes beyond the discussion we found in the Mahābhāṣya as is evident from the terminology employed -(a) sāyujyam which is not a reference to the employment of speech in daily life or in ritual; (b) a reference to ātman and to paramātman, (c) a reference to brahman -and the conceptual framework this implies. But in which direction does it go beyond the Mahābhāṣya? Not far from the already cited stanza in the Mahābhāṣya there is another stanza, this time cited from the gveda, that should express a purpose of grammar. It is V 4.58.3, catvri śṅgā … and is part of a hymn that glorifies the clarified butter (ghee) to be offered in a sacrifical fire and identifies it with Soma and with poetical speech. In the Nirukta (Nir 13.7) V 4.58.3, which speaks of a bull (vṣabha) with four horns, three feet, two heads, and of a great god who enters human beings, 7 is interpreted in terms of ritual, but in the Mahābhāṣya the bull of V 4.58.3 is grammatical speech: its four horns are four classes of words, noun, verb, preverb and particle; its three feet are the three tenses, past, present, future; its two heads are the two natures of words, the permanent and the producible, etc. The gist of the stanza according to the Mahābhāṣya is that grammar must be studied in order to have sāmyam 'similarity' or 'equality' with speech who is a mighty god.

The verse of Bharthari takes up the image of a great bull which we find in V 4.58.3. Instead of sāmyam 'similarity' or 'equality' which seems a rather neutral expression he uses a more significant word, sāyujyam 'union'. For this term there is a relevant early context with which Bharthari must have been familiar, the Brāhmaṇa and Brāhmaṇa-like portions of the Yajurvedic Saṁhitās, and especially the Upaniṣads. The index of Limaye and Vadekar's edition of Eighteen Principal Upaniṣads refers, under the word sāyujya, to places in only two Upaniṣads, the Bhad-āraṇyaka-upaniṣad and the Maitrāyaṇīya-upaniṣad. In BĀU 1.5.23, for instance, it is recommended to follow an observance (vrata) in order to achieve union with, or to live in the same world as, a deity which is, in the context of the passage, Prāṇa 'Vital Breath'. 8 In view of the relationship 7

The expression used for the entering of the god is similar to that used for Soma -juice and god -entering those who drink him, as Geldner pointed out with reference to V 1. 91.11, 8.48.12, 9.97.36, 10.16.6. 8 BĀU 1.5.23: teno etasyai devatāyai sāyujya salokatāṁ jayati; Śaṅkara, in his commentary on this passage, perhaps understands the distinction between sāyujya and salokatā as a difference in degree -as in the later series of sālokya, sāmīpya, sārūpya, sāyujya -when he says the second option, living in the same world as the desired deity, is obtained on account of a slowness in understanding: evaṃ tenānena vrata-dhāraṇena etasyā eva prāṇadevatāyāḥ sāyujyaṃ sayug-bhāvam ekātmatvaṃ salokatāṃ samāna-lokatāṃ vā ekasthānatvam -vijñāna-māndyopekṣam etat -jayati prāpnotīti. Other occurrences of sāyujya in the BĀU are 1.3.22, 5.13.1-4 where the sāyujya is obtained not by following a vrata but on account of knowledge or of understanding something in a certain way (expressed in the between Bharthari and the Maitrāyaṇī branch of the Yajurveda that can be inferred from the citations of Vedic examples, 9 the link with the Maitrāyaṇīya-upaniṣad is of special interest. In MaiU 4.1 and 4.4 the sāyujya 'union' is obtained not with a deity but whith the ātman 'self'. According to MaiU 4.4 sāyujya is obtained on account of vidyā 'knowledge' (knowledge of Brahman), tapas 'ascesis' and cintā 'reflection'. MaiU 6.22 speaks of sāyujya-tvam 'the state of being in union' which can be obtained by a meditator (abhidhyāt) in a passage that deals with two brahmans, śabda 'word' and aśabda 'non-word'. The passage contains a brief description of meditative procedures and concludes with the verse 10 dve brahmaṇī veditavye śabdabrahma paraṁ ca yat / śabda-brahmaṇi niṣṇātaḥ paraṁ brahmādhigacchati, which van Buitenen translates as "Two Brahmans are to be known, śabdabrahman and that which is beyond this. Immersed in the śabdabrahman, one attains to the Brahman beyond."

In his VP-kārikā 1.143, Bharthari uses his reference to the "Great Bull" of V 4.58.3 to refer not to the liberation or state of union (sāyujya) of a meditator (abhidhyāt) but to that of a user of language, prayokt. The root yuj in sāyujya does not refer to the employment of speech as it is rather to be understood as a reference to the Upaniṣadic concept of sāyujya. In the succeeding kārikā the goal of "union" with a deity is extended to the Upaniṣadic goal of achieving Brahman. The Vtti goes next a formula ya evaṁ veda). In the AiB 2.24 sāyujya, sarūpatā and salokatā of certain divinities is what the sacrificer is supposed to obtain in his ritual. Other Vedic occurrences of sāyujya are TS 5.7.5.7 and TB 3.9.20.9. 9 Rau 1980;[START_REF] Bronkhorst | Further remarks on Bharthari's Vedic affiliation[END_REF][START_REF] Bronkhorst | Further remarks on Bharthari's Vedic affiliation[END_REF][START_REF] Houben | Bharthari's Vākyapadīya and the Ancient Vtti (2): The Vedic background of the author of the Vākyapadīya-Vtti[END_REF]. The citation of words and phrases from Vedic literature for grammatical discussion is to be distinguished from the reference to Vedic lines in support of ideas put forward, just as the Mahābhāṣya referred to V 4.58.3. Such references are found in the MBhD and in the ancient Vtti, but quite rare. For the parallelism of an important view of Bharthari and the a view expressed in V 1.164.23-24, see Houben 2007. For Bharthari's view on the revelation of the Veda see [START_REF] Aklujkar | The Number of Kārikās in Trikāṇḍī, Book I[END_REF]2009. step further when it describes not only the goal but also the process of going towards this goal of union and that of achieving Brahman in a terminology and conceptual framework that seem close to those of the Yoga-bhāṣya. 11 It expands here the point made in VP 1.144ab that the grammatical formation of words is itself equivalent to the realisation of the ātman 'self'. In support of this expansion the Maitrāyaṇīya-Upaniṣad can be cited in its large "vulgate" recension 12 which already contains brief 11 This is a first approximation. A closer study may reveal that the VP-Vtti is still closer to another text with Yoga or Sāṁkhya background. Philosophically, the Yoga-bhāṣya works with concepts and terms of the Sāṁkhya-system (e.g. Frauwallner 1953: 408f;[START_REF] Larson | Yoga: India's Philsophy of Meditation[END_REF]; Helārāja cites a passage from the Yoga-bhāṣya on YS 2.19 as evidence for a Sāṁkhya view (VP III:42.5 on VP 3.1.34). For the closeness of the Yoga-bhāṣya and the VP-Vtti reference can be made to the use of terms which have a comparable function in both texts: puruṣa (in the Vtti often in the sense of 'man' but sometimes rather 'soul': Vtti on VP ) ; prakāśa and prakāśātman (cf. YS 2.18, 52 and their YBh; Houben 1995: 318 note 499); upasaṁhta-dhvani-krama; pratibimba; 'na sattāṁ padārtho vyabhicarati'; the word yoga when it is not referring to the employment of words in speech as in vāg-yoga-vid and śabda-pūrva yoga.

12 Bronkhorst 2009 points out similarities between the five major points he recognizes in Bharthari's thought and statements in the Maitrāyaṇīya Upaniṣad. [START_REF] Buitenen | The Maitrāyaṇīya Upaniṣad[END_REF] reconstructed an original, much shorter MaiUp and claimed that the current version contains many later additions. According to Bronkhorst (2009: 106) it would be "a priori most likely ... that Bharthari was acquainted with the original Maitrāyaṇīya Upaniṣad." However, even if we accept the results of van Buitenen's reconstruction usually on internal criteria, how likely would it be that the "late" passages were added after and not (a considerable time) before Bharthari (before late fourth / early fifth century)? Intensive engagements with ideas and practices on meditation etc. -which we also find in the chapters that have the largest number of accretions according to van Buitenen -are attested since the early centuries C.E. (Larson & Bhattacharya 2008: 67-70). If the additions would be after Bharthari one should we not expect them to reflect a more advanced level of reflection on meditative practices? Be that as it may, the passages (4.1, 4.4, 6.22) which evoke Bharthari's wording and his ideas more closely are precisely those belonging only to the "vulgate"; they are neither found in the southern version of the Maitrāyaṇīya-Upaniṣad nor are they retained in van Buitenen's reconstruction. descriptions of yogic procedures. 13 An important distinction is that the Yoga-bhāṣya does not identify the self as "word" and does not describe it in linguistic terms but relegates language to a domain outside the self. 14 The ideas on grammar and its role in the achievement and nature of liberation as expressed in the VP kārikās briefly discussed above and in the ancient Vtti on them, are already anounced in VP 1.14, esp. 14a. tad dvāram apavargasya vāṅmalānāṁ cikitsitam / pavitraṁ sarvavidyānāṁ adhividyam prakāśate // This (grammar) is the gateway to liberation (and) a therapy for impurities of speech; as the purifier of all sciences it shines in each of them.

The declaration in the first pāda that grammar is the gateway to liberation is substantiated only in 1.143-144. Moreover, the Vtti on this first pāda clearly evokes these two later kārikās and their Vtti. The very first sentence of the Vtti states that śabdapūrva yoga "the yoga of the word" is obtained by the one who knows the undivided reality (abhedatattvajña) of the specific form of the word (śabdasvarūpasya); and the next sentence speaks of obtaining "the great word-self." Later authors refer first of all to this first kārikā (VP 1.14) in order to illustrate the position of grammarians that grammar is a means for liberation. The 13 For instance, MaiU 6.22 refers not only to "two Brahmans, sound and non-sound" but also to two sorts of practices associated with these two. One seems to imply that the syllable "om" is used to reach non-sound. This is next illustrated as follows: atha yathorṇanābhis tantunordhvam utkrānto 'vakāśaṁ labhatīty evaṁ vāva khalv asā abhidhyātom ity anenordhvam utkrāntaḥ svātantryaṁ labhate; Buitenen interprets abhidhyāt as "the yogin in meditation" and translates "Just as a spider climbing up along its thread finds open space, so indeed the yogin in meditation climbs up through OM and finds complete independence." Ideas and illustrations such as these are still far removed from the systematic and technical discussions in the Yogabhāṣya.

14

That is what we can infer from YS 3.17 and Bhāṣya and the definition of the state of liberation (kaivalya) in YS 4.34 and Bhāṣya.

his statement that grammar is the cause for heaven and liberation (tasya ... svargamokṣādihetutvam).

In his Śabdakaustubha, a commentary on (parts of) the Aṣṭādhyāyī and paying much attention to the Mahābhāṣya, Bhaṭṭoji-dīkṣita cites ekaḥ śabdaḥ … and yas tu prayuṅkte … but does not elaborate on their significance (MBh ed. (b) p. 28). To the g-vedic verse that was cited in the MBh and that gave occasion to Bharthari to compose his 1.143 api prayoktur … Bhaṭṭoji refers very briefly (together with other Vedic verses) without further discussion: gvede'pi bahavo mantravarṇāḥcatvāri śṅgā, catvāri vāk, uta tvaḥ paśyan, saktum ivetyādayaḥ (MBh ed. (b) p. 32).

A century or so later, Nāgeśa in his Uddyota on catvri śṅgā … does cite VP 1.143 and explains it with a citation-cumgloss of part of the Vtti on VP 1.143. In his Laghu-mañjūṣā Nāgeśa expresses as his view that the employment of language after knowing its analysis by grammar leads to purity of the mind and brings about liberation (… jñānapūrvakaprayogasya cittaśuddhidvārā apavargasaṁpādanatvena śāstrajñ ānasya āvaśyakatvāt cited after Abhyankar & Limaye 1965: 200), which confirms his positive acceptance of the ideas expressed for the first time most clearly in the VP-Vtti on VP 1.14, 143-144.

3.4 From the preceding discussion we retain the following points. (a) In the Mahābhāṣya grammar has a function with regard to reaching some blessed state expressed in terms of Vedic religiosity. Forms of yuj in this context refer to the employment of speech in daily communication and in (Vedic) ritual. (b) In the VP-kārikās references are found to the efficacy of grammar with regard to religious or spiritual aims. The sāmya 'similarity' between "us" and the deity of speech in the Mahābhāṣya (in a special interpretation of V 4.58.3), is replaced by the Upaniṣadic sāyujya 'union' in VP 1.143. (c) Unlike the Maitrāyaṇīya-upaniṣad and even more unlike a text such as the Yoga-bhāṣya, the VP-kārikās pay no attention to process or procedure: this we find in the VP-Vtti, esp. on VP 1.14, 1.143-144. An important distinction with the Yoga-bhāṣya, which clarifies the peculiar position of the VP-Vtti and apparently of the later grammarians, is that for the Yoga-bhāsya "language" remains distant from the "self" whereas the VP-Vtti, following the indications in the VP-kārikās, identifies the two.

4.1 Although the peculiar position regarding grammar and liberation found in the VP-kārikās and Vtti has been identified as THE view of the Pāṇinian grammarians (as we saw in the Sarvadarśanasaṁgraha), and although there are indeed starting points for this position in the Mahābhāṣya of Patañjali, this is not the only Pāṇinian position adhered to by the grammarians of ancient and pre-modern India. Apart from the traditional line followed in the preceding discussion -from Patañjali to Bharthari and Bhaṭṭoji-dīkṣita and finally Nāgeśa -there is another traditional line which was hardly less important although it has received less attention in modern research. For this other line, Patañjali's Mahābhāṣya is known and appreciated but no attempt is made to place it on an absolute footing as in the school of Bhaṭṭoji and his followers. This other line is the pragmaticrather than exegetical and theoretical -grammatical tradition of which the Kāśikā (7 th cent.) is the oldest extensive representative and that was continued in Kerala in the work of Melputtūr Nārāyaṇa-bhaṭṭa who was roughly contemporaneous to Bhaṭṭojibhaṭṭa (16 th / 17 th century).

With regard to the topic under discussion, a possible link between grammar and liberation, we can be brief about the Kāśikā: it is absolutely disinterested and does not speak about it. After its introductory verse announcing the topic and textual context, 17 the Kāśikā immediately proceeds with the technical problems in understanding and applying the sūtras of Pāṇini. 17 It has now been argued, mainly on the basis of the evidence provided by the earliest commentaries, that only the first of three generally accepted introductory verses is authentic [START_REF] Haag | Paratextual Elements in Indian Manuscripts: the Copyists' Invocations and the Incipit of the Kāśikāvṛtti[END_REF] 4.2 The little-known Prakriyā-sarvasva (PS) by the brilliant and versatile author Nārāyaṇa-bhaṭṭa of Melputtūr remains in several respects close to the Kāśikā, although it is mainly the grammar of Bhoja that is now and then praised by Nārāyaṇa. In any case the PS is quite unattached to Patañjali even if Nārāyaṇa is evidently familar with his work. Although in the view of the orthodoxy of the school of Bhaṭṭoji and Nāgeśa, the PS of Nārāyaṇa may seem un-pāṇinian, it is thoroughly pāṇinian according to Nārāyaṇa's own statement. In introductory verse no. 9 (a Gīti), Nārāyaṇa-bhaṭṭa explicitly acknowledges his teacher Acyuta (Piṣāroṭi) and the ancient grammarians Pāṇini and Kātyāyana; Patañjali and other ancient grammarians are apparently implied in ādi: ayam acyuta-guru-kpayā pāṇini-kātyāyanādi-kāruṇyāt / yatnaḥ phala-prasūḥ syāt kta-rāga-raso 'dya śabda-mārga-juṣām // Through the compassion of the teacher Acyuta (Piṣāroṭi) and on account of the kindheartedness of Pāṇini, Kātyāyana and others, this effort should be fruitful -this effort which has as essence (rasa) a passion (rāga) that is today accomplished (kta) for those enjoying the way of words.

The PS is at least as comprehensive as the well-known grammar of Bhaṭṭoji-dīkṣita, the Siddhānta-kaumudī, but significantly differs from it in both method and substance, even if both remain within the framework of Pāṇini's system. The features of the PS are contrasted with those of other works, and its substance are explained in introductory verses 5 (Śārdūlavikrīḍita) and 6-7 (two Gītis), which are placed in the mouth of Nārāyaṇa's sponsor, the king Devanārāyaṇa of Ampalapuḻa. At present verse 5 is of interest as it contextualizes the Prakriyā-sarvasva: vttau cāru na rūpasiddhi-kathanā [>naṁ] rūpāvatāre punaḥ kaumudyādiṣu cātra sūtram akhilaṁ nāsty eva tasmāt tvayā / rūpānīti-samasta-sūtra-sahitaṁ spaṣṭaṁ mitaṁ prakriyā-sarvasvābhihitaṁ nibandhanaṁ idaṁ kāryaṁ mad-uktādhvanā // In the (Kāśikā-)Vtti the description of the formation of the form (of words) is not nice ; and again in the Rūpāvatāra (of Dharmakīrti) and in works such as the (Prakriyā-) kaumudī (of Rāmacandra), in these the text of the sūtras is not complete ; that is why you (Nārāyaṇa Bhaṭṭa) should compose, according to the way which I (Devanārāyaṇa) tell you (in the next verses in which I sum up the 20 chapters), this clear and well-measured work called Prakriyā-sarvasva that contains all sūtras and the formation of forms."

Although the PS is pāṇinian in substance and method, Nārāyaṇa explicitly argues that Pāṇini's authority is not absolute. At the end of chapter 11 on verbal endings, Nārāyaṇa gives a verse (in the Sragdharā metre) that, in a nutshell, explains his position in a controversy with a scholar (probably from the Tanjavur court) who placed much emphasis on the authoritativeness of Pāṇini. The same verse appears again at the beginning of the Apāṇinīyapramāṇatā (AP) where the argument is expanded. The position which Nārāyaṇa does not accept is: pāṇinyuktaṁ pramāṇaṁ, na tu punar aparaṁ candra-bhojādi-sūtram, "Authoritative is (exclusively) what Pāṇini said, but not the other grammars of Candra, Bhoja etc." The arguments Nārāyaṇa gives to disagree with this include: (a) na khalu bahuvidām asti nirmūla-vākyam, "Indeed, by persons (such as Candra and Bhoja) who know much no base-less statement is passed. (Hence, the grammars of Candra, Bhoja etc. cannot be dismissed just like that)"; pāṇineḥ prāk kathaṁ vā, "And how was the situation (with regard to linguistic correctness) before Pāṇini? (Even without Pāṇini's grammar people could speak correct Sanskrit)"; pūrvoktaṁ pāṇiniś cāpy anu-vadati, "And Pāṇini (himself) repeats what has been said by predecessors (and thus accepts their authority)"; virodhe 'pi kalpyo vikalpaḥ, "Even if there is a contradiction (between other authorities and Pāṇini) a (grammatical) option is to be created (so that the non-Pāṇinian grammarian need not be rejected)." Nārāyaṇa's attitude is remarkably rational and historically realistic and contrasts with Bhaṭṭoji's decision that there is no correct Sanskrit after the three sages whose authoritativeness is absolute and who are placed on a divine level. In this sense there is no interference of theology in grammar in the case of Nārāyaṇa's work. This can also be inferred from the fact that for Nārāyaṇa the pratyāhāra-sūtras are not composed by the god Śiva as is the generally accepted view in Bhaṭṭoji's school (where these sūtras are called Śiva-sūtras or Māheśvarasūtras).18 4.3 Grammatical examples, however, are often original statements taken from the life of Kṣṇa and frequently of remarkable poetic beauty. This starts with the first introductory verse (Gīti) which is not just a simple reference to the rāsadance of Kṣṇa and the Gopīs (cowherd women): it presents the relationship between Kṣṇa and the Gopīs as a mirror of the relationship of base and affixes. rāsavilāsavilolaṁ smarata murārer manoramaṁ rūpam / praktiṣu yat pratyayavat pratyekaṁ gopikāsu saṁmilitam // Bring to mind the charming form of Murāri (Kṣṇa), going round in the playful rāsa-dance, (the form of Kṣṇa which) like the (male) suffix to the (feminine) verbal themes, is unified, one by one, with each of the Gopīs.

As for the opposition Dvaita versus Advaita Vedānta which was of some importance for Bhaṭṭoji-dīkṣita, Melputtūr Nārāyaṇa Bhaṭṭa is fully engaged in the bhakti-mārga which presupposes a dualistic outlook, but he speaks with sincere respect of the Advaita Vedāntist Śaṅkara 19 and in the Apāṇinīya-pramāṇatā (AP) he defends the correctness of one of Śaṅkara's "unpāṇinian" verb-forms: hunet (instead of juhuyāt). Another dichotomy in disputes in which Bhaṭṭoji-dīkṣita was engaged concerned Vaiṣṇava bhakti and the adherence to Vedic ritual. In the case of Nārāyaṇa the two are harmoniously combined. There is no sign that Nārāyaṇa's enthousiasm for Vaiṣṇava bhakti interfered with his engagement in Vedic ritual or with his interest in Mīmāṁsā.

Since theology is basically a sphere that is different from grammar that remains limited to the content of examples and illustrations, there is for Nārāyaṇa-bhaṭṭa little overlap and no occasion either to discuss their possible link or to end up in a dispute with non-grammarian philosophers who feel that their domain is encroached upon by the grammarians.

Nevertheless, at the end of chapter 17 on "principles of interpretation" which is also the end of the first major part (pūrvabhāga) of the entire grammar and which precedes the long technical discussions that have to constitute the second major part (uttarabhāga) consisting of the chapters on the Dhātupāṭha, the Uṇādi-suffixes and the Chāndasa-grammar, Nārāyaṇa pours out his heart in the following verse in the Śārdūlavikrīḍita metre: āstām anyad ihārthaśabda-paṭalīṁ tac-cintanādi-kriyāṁ śabda-vyākti-janya-puṇya-nivahaṁ pāpaṁ ca vāg-doṣajam / sarvaṁ tat prajuhomi nanda-tanaye mandasmitārdrānane pūrṇa-brahmaṇi ; tūrṇam eṣa karuṇā -sindhur mayi prīyatām // Let the rest (other possible principles of interpretation as discussed in chapter 17) remain. --Here the veil of words and meanings, (mental) activities such as thinking about them, the mass of merit produced by the analytic formation (vy-ā-kti) of words, and the demerit arising from mistakes in the language : of all that I make an offering to the son of Nanda (that is, to Kṣṇa), whose tender face has a faint smile : to (him who is no-one else but) the complete Brahman ; may that river of compassion quickly find satisfaction in me.

At the end of the long first major part of his work, Nārāyaṇa's mind shifts as it were to another gear: linguistic items and their meanings, the action of reflecting on them, the analytic formation of words (according to the rules of grammar), merit and demerit arising from the use of correct and incorrect words -they are all given up and transferred to Kṣṇa, whom he regards as the basis of the universe, Brahman (neuter). The verse expresses the aim to come out of an excess of intellectual activity and to become one with, or at least to become close to, either the personal Kṣṇa in the guise of the neutral Brahman or, vice versa, the neutral Brahman in the guise of the personal Kṣṇa. As such it brings to mind, on the one hand, the concept of citta-vtti-nirodha (YS 1.2), the stopping of (some or all) specific modes of functioning of the mind; and, on the other hand, the concept of yoga to be attained by an optional devotion to Īśvara, īśvara-praṇidhānād vā (YS 1.23).

4.4 From our discussion of Nārāyaṇa-bhaṭṭa's grammar the following points can be retained. (a) No link is suggested between the correct employment of speech in daily communication and in (Vedic) ritual and the achievement of a blessed state expressed in terms of Vedic religiosity, to which the Mahābhāṣya hinted. It is admitted that correct speech leads to some merit, which, however, is insignificant in the light of the result to be expected from devotion to Kṣṇa. (b) There is therefore also no reference to any efficacy of grammar with regard to religious or spiritual aims (except for the apparently quite insignificant merit that comes from using correct speech). More generally, although Nārāyaṇa does not make it an explicit topic of his discussion, his occasional devotional expressions, esp. the one studied in the second part of paragraph 4.3, rule out the position of linguistic non-dualism for which Bharthari had become famous, which was accepted by Bhaṭṭoji-dīkṣita, the grammarian contemporaneous with Nārāyaṇa Bhaṭṭa, and which was again embraced by Bhaṭṭojidīkṣita's successors.

(c) Nārāyaṇa-bhaṭṭa shows little interest in the ideas, aims and practices of the Yoga-system except for the option of devotion; however, he is basically in agreement with the Yoga-bhāṣya when he posits "language" and grammatical reflection about it as distant from the "self" which desires to get close to Kṣṇa or Brahman. Here, Nārāyaṇa's position and that of the Yogabhāṣya converge and are diametrically opposed to that of the VP-Vtti which, following the indications in the VP-kārikās, identifies the ātman and śabda, the "self" and the "word." In addition, for Nārāyaṇa and Yoga-bhāṣya language means a plurality of words, there is no attempt to represent it as somehow "one" (which leads to forced renderings of śabda, normally 'word', as language-principle, or as Word with capital, etc.). 5. Whatever the comparison of a few marginal and two central lines of thought on grammar may have revealed, it is clear that the Indian grammatical tradition shows considerable internal diversity not only in technical aspects but also with regard to reflections on the place of grammar in a larger framework of philosophical and religious thought.

For Bharthari language has a universal, non-dual aspect which is identical with the self of the speaker and which the speaker has to try to bring to perfection; for Nārāyaṇa-bhaṭṭa language is a mode of the mind that can be suspended or given up. With regard to the major tradition of grammar from Patañjali via Bharthari to Bhaṭṭoji-dīkṣita and Nāgeśa, comparisons along the lines sketched here can be expected to bring into sharper relief the peculiarity of some of its philosophical and religious decisions at the background of its scientific practice.

 Iyer 1969: 9-10, 407; Torella 2002: xixf ; 2009.

 Joshi and Roodbergen, 1986: 43, accordingly translate kuśala as "being knowledgeable."

This verse also occurs in the Mahābhārata and has been retained in the critical edition where it is found in the Śāntiparvan, 224.60.

Deshpande

Cf. Kunjunni Raja 1958: 140f.

of Sāyaṇa-mādhava (14 th cent.) cites VP 1.14 (and VP 1.16 which is part of the Vtti 15 ) in order to support the statement that the science of grammar is a means to liberation (śabdānuśāsanaśāstrasya niḥśreyasasādhanatvaṁ siddham).

3.3 Bhaṭṭoji-dīkṣita (16 th /17 th cent.) made major efforts to reestablish the Pāṇinian grammatical tradition by following more strictly than his immediate predecessors three ancient grammarians: Pāṇini, Kātyāyana and Patañjali (cf. [START_REF] Houben | Bharthari's Vākyapadīya and the Ancient Vtti (2): The Vedic background of the author of the Vākyapadīya-Vtti[END_REF]. These three grammarians, the three sages (muni-traya), are placed on a level of absolute authoritativeness in grammatical matters. From introductory verses and from nongrammatical works of Bhaṭṭoji we can infer that he also had specific ideas on religious practice and liberation. 16 In his Tattvakaustubha, for instance, we find a defence of Advaita Vedānta against Dvaita ideas and also a defence of Vedic ritual against Vaiṣṇava preferences of bhakti. However, that grammar would be able to play an important role in obtaining liberation is accepted by him but he does not pay much attention to it at places where we would expect this.

In his VSK Bhaṭṭoji discusses the established views of grammarians on grammatical and theoretical issues. A few kārikās of Bharthari are adopted as kārikās of this work that is known in two different forms, one -the best known onecommented upon by Kauṇḍa-bhaṭṭa and the other by Vanamālimiśra. VP kārikās 1.14 and 1.143-144 are not among the VPkārikās integrated in his text. Other VP-kārikās are cited by Kauṇḍa-bhaṭṭa in his commentary. Under VSK 69 pañcakośādivat ... Kauṇḍa-bhaṭṭa refers to VP 1.14 to support 15 If we apply the two criteria that a verse should not be explicitly said to be a citation and that it must have been commented upon as a kārikā in the Vtti in order to be accepted as a kārikā (cf. Iyer 1966 : x), VP 1.16 must be relegated to the Vtti (Aklujkar 1971 : 510).

16 More details on technical and contextual factors of Nārāyaṇabhaṭṭa's Prakriyā-sarvasva I discussed in Houben, forthcoming. A fundamental study is still Venkitasubramonia Iyer 1972.