# VIPA based high-contrast high-efficiency two-stage Brillouin imaging spectrometer using a single diffraction mask

Alban Desoutter, Rémy Vialla, Frédéric Cuisinier, Yassine Messat, Hamideh Salehi, Emmanuel Rousseau, Benoit Rufflé

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Alban Desoutter, Rémy Vialla, Frédéric Cuisinier, Yassine Messat, Hamideh Salehi, et al., VIPA based high-contrast high-efficiency two-stage Brillouin imaging spectrometer using a single diffraction mask. Journal of Applied Physics, 2025, 138 (4), pp.044702. 10.1063/5.0274757. hal-05248517

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Submitted on 10 Sep 2025

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This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0274757

VIPA based high-contrast high-efficiency two-stage Brillouin imaging spectrometer

using a single diffraction mask

Alban Desoutter¹, Remy Vialla², Frédéric Cuisinier¹, Yassine Messat¹, Hamideh Salehi¹,
Emmanuel Rousseau², Benoit Rufflé²

¹ LBN, Univ. Montpellier, Montpellier, France

² Laboratoire Charles Coulomb, UMR 5221 CNRS-Université de Montpellier, FR-34095 Montpellier, France

Corresponding author: Benoit Rufflé, benoit.ruffle@umontpellier.fr

**Abstract**

Brillouin spectroscopy is a non-invasive method technique for visualizing the mechanical properties of biological samples with sub-micron resolution. However, to obtain 2D or even 3D maps, a high-contrast spectrometer is required to effectively reject spurious signals and isolate the signal of interest. In this work, we present an optimized two-stage VIPA-based Brillouin spectrometer capable of achieving a contrast of at least 80 dB thanks to a new single diffraction mask, and thus with an unprecedented high overall transmission. Numerical simulations of the electric field propagation through the spectrometer and dedicated experiments validate the increase in contrast. We have used the newly developed Brillouin spectrometer coupled to a confocal microscope to obtain one-hour high-resolution 2D images of about 10⁴ spectra of transparent dental pulp stem cells near a MgF₂ interface as well as of the much less transparent porcine dentin material, demonstrating its overall stability and reliability.

**Keywords:** Brillouin Scattering, Spectrometers, VIPA, contrast, diffraction mask.
# 1. Introduction

The need to understand the mechanical properties of cells and tissues has led biologists and biophysicists to develop Brillouin scattering microscopy [1-7]. Indeed, the mechanical properties of a material can be deduced from the spectrum of the light it scatters. When illuminated with monochromatic light, the backscattered spectrum of an isotropic material exhibits three distinct peaks: a central peak at the frequency of the incident light and two weaker satellite peaks symmetrically positioned on either side. The central peak arises from the elastic scattering of the incident light, known as Rayleigh scattering, which retains the same frequency as the incident light. The satellite peaks, on the other hand, result from interactions between the incident light and the vibrational modes of the material. These are referred to as Brillouin peaks, named after Léon Brillouin, who first explained this phenomenon [8]. Brillouin scattering is an inelastic process that modifies the energy of the scattered light: one Brillouin peak corresponds to a slight energy gain relative to the incident light, while the other corresponds to an equivalent energy loss. Consequently, the Brillouin peaks are symmetrically offset from the Rayleigh peak in frequency. The magnitude of the Brillouin frequency shift is directly related to the mechanical and optical properties of the material and the wavelength of the incident light. By analyzing the position, intensity and width of these Brillouin peaks, valuable insights into the material's elastic moduli and other mechanical properties can be obtained.

Brillouin light scattering poses a significant challenge due to the need for high frequency resolution and high contrast to discriminate the Brillouin peaks from the Rayleigh scattering. In fact, the Brillouin peaks are typically shifted by ~$10^{-5} f_0 - 10^{-4} f_0$, where $f_0$ is the incident light frequency, while their relative intensity is often orders of magnitude lower. These limitations were largely overcome fifty years ago by J. Sandercock who developed a versatile multi-pass tandem spectrometer based on planar Fabry-Perot interferometers [9]. This configuration has since become the gold standard for Brillouin light scattering in physics laboratories. However, the Brillouin spectrum is typically obtained by scanning the Fabry-Perot etalons a few dozen times. Since it takes about half a minute to acquire each spectrum, a 2D image of the viscoelastic properties of a sample with a thousand spectra takes about eight hours, which is not practicable with biological samples [10-12].

In recent years, technological advances have led to a new class of Brillouin spectrometers based on an innovative solid Fabry-Perot etalon, the so-called Virtually Imaged Phased Array (VIPA)
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
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[13]. The latter is used in a dispersive configuration to obtain a Brillouin spectrum in a single shot. Compared to a standard scanning interferometer, dispersive instruments are known to significantly improve the acquisition time by a factor of about 60, given by the etalon's fineness [14-17]. Currently, Brillouin spectrometers based on VIPA etalons enable the acquisition of spectra in about 100 ms. However, this improved efficiency, in terms of the time required to acquire a single spectrum, comes at the expense of the frequency resolution and, more importantly for biomaterials, the contrast of the spectrometer. The latter is defined as the ratio between the maximum and minimum transmittance and is often expressed in dB. The contrast of a spectrometer is a fundamental parameter in the design of a Brillouin spectrometer. It is an intrinsic property of the spectrometer itself and remains independent of the light scattering processes being observed. The transmission of light through a Fabry-Perot interferometer is characterized by distinct transmission peaks at specific wavelengths, which are determined by the properties of the interferometer. Since Rayleigh and Brillouin scattering occur at slightly different frequencies, the transmission of light from Rayleigh scattering does not perfectly overlap with that from Brillouin scattering. As a result, despite the inherently low intensity of Brillouin scattering, it is possible to distinguish it from Rayleigh scattering if the Brillouin peak at its maximum intensity exceeds the Rayleigh component at its minimum intensity. This ability to distinguish between the two is quantified by the contrast of the spectrometer.

While the contrast for standard six-pass tandem interferometers is at least 120 dB, it is only 30 dB for a single-stage VIPA-based spectrometer and about 55 dB for a two-stage one. A single VIPA is generally unable to distinguish the weak Brillouin signal from the strong elastically scattered signal due to interfaces or the sample itself. Two cascaded VIPAs have proven sufficient to measure Brillouin peaks in transparent materials far from interfaces, such as cells and polymers [18-20]. However, this setup is generally not suitable for experiments that generate large amounts of elastic scattering. Over the last decades, many proposals have been made to increase the contrast of VIPA-based spectrometers or, alternatively, to reduce the intensity of the elastically scattered light entering the spectrometer. Among them, molecular absorption cells [21-22], planar etalon prefilters [23-24], common path interferometric filtering [25-26], destructive interference [27], Michelson interferometer [28] or birefringence-induced phase retardation [29] have been used to selectively eliminate the unshifted scattered light with an efficiency between 20 and 50 dB at reasonable insertion losses. These devices require constant control during the experiment to ensure optimal efficiency, which complicates the setup. On the other hand, the intrinsic contrast of VIPA-based spectrometers can be increased
by various light wave manipulations such as apodization [1,30], Fourier masking [31-33] or even both [31], but at the expense of complexity, stability and overall transmission of the spectrometer. These advances, combined with confocal microscopy, have enabled Brillouin imaging spectroscopy to be used in multiple applications in biomedical sciences [34]. Preliminary Brillouin images of cells have prompted an increasing number of studies on cell mechanobiology [1,3,35-43] as well as on tissues [44-47] just to cite a few.

In this paper, we present an optimized two-stage VIPA-based Brillouin spectrometer that achieves a contrast of at least 80 dB thanks to a single diffraction mask, and thus with an unprecedented high overall transmission. The spectrometer is based on a setup originally proposed by E. Edrei et al. [31]. Numerical simulations of the electric field propagation through the spectrometer and dedicated experiments validate the increase in contrast and transmission. Coupled to a confocal microscope, the Brillouin spectrometer was used to obtain a one-hour high-resolution 2D image of about 10⁴ spectra of transparent dental pulp stem cells near a MgF₂ interface, demonstrating its overall stability. To further demonstrate the capabilities of our setup we succeeded in obtaining similar Brillouin images of the much less transparent porcine dentin material.

## 2. Brillouin scattering and mechanical properties

As explained in the introduction, Brillouin scattering can assess the mechanical properties of materials. In this paper, we focus the discussion on biological cells that are mainly made of water. For our purpose, it is then sufficient to consider a liquid as the materials to understand the main principles of our instrument. In a liquid, the spectrum of the scattered light consists of a symmetrical pair of peaks, called Brillouin peaks, on either side of the elastically scattered light. The spectrum of Brillouin scattered light provides information about the local mechanical properties of the liquid under study. In fact, the Brillouin frequency shift $v_B$ is related to the sound velocity $v$ of the liquid and the real part $K'$ of the complex bulk modulus $K = K' + iK''$ through

$$v_B = \frac{2nv}{\lambda_0} \sin \frac{\theta}{2} \qquad K' = \rho v^2 \qquad (1)$$

where $n$ and $\rho$ are the refractive index and the density of the liquid, respectively, while $\lambda_0$ is the wavelength in vacuum of the incident light and $\theta$ the scattering angle. Furthermore, the linewidth $\Gamma_B$ of the Brillouin peak (full width at half maximum) is related to the dynamic bulk viscosity $\eta_K$ and the imaginary part $K''$ through
$$ \Gamma_B = 2\pi\eta_K \frac{v_B^2}{K'} \qquad K'' = 2\pi\eta_K v_B \qquad (2) $$

For an isotropic solid, replace K with the longitudinal modulus $M = K + \frac{4}{3}G$, where G is the shear modulus, and $\eta_K$ with the longitudinal viscosity $\eta_L = \eta_K + \frac{4}{3}\eta_S$, where $\eta_S$ is the shear viscosity.

### 3. Numerical simulations

We performed numerical simulations of light field propagation through the VIPA spectrometer using the standard Angular Spectrum Method (ASM), which provides simple expressions relating the object and image complex fields [48]. The ASM is a powerful method for describing light beam propagation and light focusing. It uses the Fourier transform which converts spatial coordinates $(x, y)$ into spatial frequencies $(k_x, k_y)$. We modeled all the optical elements present in the spectrometer, including spherical lenses, cylindrical lenses, and VIPAs. The modeling also requires accounting for free space propagation to accurately describe the relative phase difference between input light source and the CMOS camera. The main advantage of the ASM for this problem is its simplicity; it only requires computing a series of Fourier transforms. This computation is efficiently performed using the FFT algorithm. The model neglects polarization effects and assumes the electric field is a scalar quantity, $E(x, y, z)$ that depends on the three spatial variables. The ASM describes this electric field through a two-dimensional inverse Fourier transform:

$$ E(x, y, z) = \int_{\mathbb{R}^2} dk_x dk_y \hat{E}(k_x, k_y, z) e^{j(k_x x + k_y y + k_z z)} e^{-j\omega t} \qquad (3) $$

The electric field is assumed to be monochromatic, with angular frequency $\omega$. The Fourier transform is restricted to a plane thanks to a dispersion relation relating the angular frequency and the components of the wave vector $\vec{k}$, $(k_x, k_y, k_z)$.

In free space, the dispersion relation is $k_x^2 + k_y^2 + k_z^2 = \omega^2/c^2$, which enables to express $k_z$ as a function of $k_x, k_y$ and $\omega = ck$. The propagation direction along the optical axis is chosen to be the positive z-axis. Figure 1 depicts the methodology to compute the electric field amplitude using ASM for free space propagation (a), VIPA (b) and spherical lens (c).
<figure><img src="image_2.png" /><figcaption>Figure 1: Sketch of the principles of the angular spectrum method for computing light propagation for a) free space propagation from z = 0 to z = L, b) propagation through a VIPA between the input mirror located at z = 0 and the output mirror at z = e (the VIPA is inclined at an angle α to the horizontal axis of rotation), c) propagation through a thin lens between the object and image focal planes located at z = -f and z = +f, respectively.</figcaption></figure>

To calculate the propagation of the field in free space from the z = 0 to z = L, a 2D Fourier transform is first applied on the field amplitude $E(x, y, 0)$. Then, each plane wave, with amplitude $\hat{E}(k_x, k_y, 0)$, is propagated to the plane z = L. The propagation of a plane wave reduces to its multiplication by the free space transfer function [48]:

$$H_{fs}(k_x, k_y, L) = e^{jL\sqrt{(\omega/c)^2 - (k_x^2 + k_y^2)}} \quad (4)$$

To find the field amplitude at the z = L plane, $E(x, y, L)$, an inverse Fourier transform is taken:

$$E(x, y, L) = \int_{\mathbb{R}^2} dk_x dk_y \hat{E}(k_x, k_y, 0) H_{fs}(k_x, k_y, L) e^{j(k_x x + k_y y)} \quad (5)$$

The methodology for computing propagation through a tilted VIPA etalon, Figure 1-b, is similar to that in free space except that multiplication by the free space transfer function $H_{fs}(k_x, k_y, L)$ is replaced by multiplication by the transfer function of a tilted Fabry-Perot etalon $H_e(k_x, k_y, e)$ [49,50]:

$$H_e(k_x, k_y, e) = t_1 t_2 \frac{e^{j e \sqrt{n^2 k^2 - (k_x^2 + k_y^2)}}}{1 - r_1 r_2 e^{j 2e \left( \cos \frac{\alpha}{n} \sqrt{n^2 k^2 - (k_x^2 + k_y^2)} - k_y \sin \frac{\alpha}{n} \right)}} \quad (6)$$

where α is the small tilt angle to the x-axis of rotation, e the thickness of the etalon and n its refractive index. $t_1$ and $r_1$ are the transmission and reflection amplitudes of the first reflecting mirror. $t_2$ and $r_2$ are the transmission and reflection amplitudes of the second reflecting mirror.
Due to the specific nature of the solid VIPA etalon, which uses a nearly transparent entrance window, $t_1$ is replaced by unity in Eq. 6. For our simulations we used $r_1 = \sqrt{0.99}$, $r_2 = \sqrt{0.93}$, $t_2 = \sqrt{1-r_2^2}$, $e = 3.37$ mm, $n = 1.4607$ and $\alpha = 1.292^\circ$ for the two VIPAs. The field amplitude at the output mirror plane $z = e$, $E(x, y, e)$, is obtained via an inverse Fourier transform:

$$E(x, y, e) = \int_{\mathbb{R}^2} dk_x dk_y \hat{E}(k_x, k_y, 0) H_e(k_x, k_y, L) e^{j(k_x x + k_y y)} \quad (7)$$

Finally, we describe how to compute the field amplitude, $E(u, v, f)$, in the image focal plane of a thin lens with focal length $f$. According to the Fraunhofer approximation, the field amplitude is given by [48]:

$$E(u, v, f) \propto \int_{\mathbb{R}^2} P(x, y) E(x, y, -f) e^{-jk \frac{xu+vy}{f}} dxdy \quad (8)$$

where $P(x, y)$ is a potential pupil, like slits or masks, that modifies the amplitude of the electric field in the plane $z = -f$. Since we are only interested in intensity of the electric field, $|E|^2$, we do not account for the phase factor in front of Eq. 8. We observe that Eq. 8 is nothing else than a Fourier transform of the quantity $P(x, y)E(x, y, -f)$. Therefore, only one FFT is needed to compute the electric field amplitude in the image focal plane of a thin lens. When modeling light propagation through a cylindrical lens, we used Eq. 8 with $f \to +\infty$ in one direction. We assume that all lenses are perfect with a focal length of 200 mm.

We sampled the light field in each plane using a uniform grid of 2048 × 2048 pixels that covered a 24 × 24 mm² square. This was necessary to properly capture the spatial dispersion of the light field after the VIPAs. The initial light source consists of three monochromatic Airy beams, each with a 2 mm diameter at the object plane of the first cylindrical lens. One beam is for the Rayleigh component (with a wavelength $\lambda = 532$ nm), and the other two are for the Brillouin doublet (with wavelengths $\lambda_{\pm} = \lambda \pm \Delta\lambda$, where $\Delta\lambda = 7.1$ pm). Since these three components have different wavelengths, they must be treated independently. Similar results are obtained using initial Gaussian beams, though transmission through the VIPAs is slightly better. The numerical simulations were performed using MATLAB, a commercial mathematical software package for Windows.

## 4. High-contrast high-efficiency Brillouin imaging spectrometer

High-resolution imaging of biological materials is typically performed using a Brillouin spectrometer coupled to a confocal microscope to collect the backscattered light. In this
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
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scattering geometry, turbid samples or transparent samples near an interface can produce strong elastic scattering that can mask the Brillouin peaks. This occurs when the ratio of the two components, namely the magnitude of the Rayleigh scattered light and the magnitude of the Brillouin scattered light, exceeds the contrast of the Brillouin spectrometer. To perform Brillouin imaging in this configuration, a spectrometer with a high contrast and a high transmission is required.

Figure 2 shows the optical setup of the Brillouin spectrometer. The incident light beam is a single longitudinal laser mode with a center wavelength $\lambda_0 \approx 532$ nm and spectral width of less than 1 fm. The beam is expanded to cover the objective pupil of the microscope. The light scattered by the sample is collected by the same objective and focused on a pinhole spatial filter by a spherical lens of focal length $f = 500$ mm, forming a confocal system. The light exiting the pinhole is collimated by a spherical lens of focal length $f = 150$ mm and directed to the Brillouin spectrometer.

<figure><img src="image_3.png" /><figcaption>Figure 2: Scheme of the confocal Brillouin imaging spectrometer.</figcaption></figure>
The Brillouin spectrometer is based on two equivalent stages, each consisting of a VIPA (free spectral range 30 GHz, Light Machinery) and a slit with focusing and collecting lenses. The main but important difference between the two stages is the orientation of the VIPA and the slit, where the orientation of the slit and the VIPA of the second stage is rotated by 90 degrees compared to the orientation of the slit and the VIPA of the first stage. The different orientations of the two stages allow the light to be dispersed in the two directions transverse to the main direction of the light propagation, a configuration originally proposed by Scarcelli & Yun [20]. Consequently, we use cylindrical lenses (CL1 and CL2) with focal lengths of f = 200 mm for the first stage while we use spherical lenses (SL1 and SL2) also with focal lengths f = 200 mm for the second stage. The spectral pattern at the output of the second stage is imaged onto a CMOS camera (Kuro 1200, Princeton Instruments) using two spherical lenses (SL3, f = 50 mm and SL4, f = 200 mm) leading to a four times magnification required for the light beam to cover the CCD sensor. A diffraction mask is placed in the Fourier plane of SL3 to significantly improve the contrast of the spectrometer with almost no loss of the Brillouin intensity, as discussed below and first proposed by Edrei et al. [31].

**5. Diffraction mask principle**

Two-stage VIPA-based Brillouin spectrometers typically show only two Brillouin peaks, a Stokes and an anti-Stokes peak, originating from two consecutive orders. This is achieved by physically blocking all intense Rayleigh peaks with the horizontal and vertical slits to avoid saturation of the detector, which also blocks all other Brillouin peaks. In the plane of the slits, the Brillouin and Rayleigh peaks are spatially well separated, allowing a large part of the elastic scattered signal to be easily removed. However, the periodic transmission of the VIPA, which is characterized by the Airy function, decreases slowly between orders. The contrast is typically about 55 dB for two VIPA. When examining turbid samples or transparent samples near an interface with a refractive index mismatch, this contrast can become insufficient to clearly observe the expected Brillouin peaks. Adapting the principle of Lyot coronagraphs, Edrei et al. showed that a closing circular Lyot stop placed at the focal plane of SL3 could increase the contrast of their two-stage apodized VIPA spectrometer up to about 80 dB [31]. This section explains how a simple two-stage VIPA spectrometer with a different diffraction mask can achieve this high contrast with better transmission.
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All the lenses of the Brillouin spectrometer are arranged in a 4f configuration with optical components, such as VIPA, slit or diffraction mask, positioned in the focal plane of the previous and next lens. Consequently, the light field at the image focal plane of a lens is the Fourier transform of the light field at the object focal plane of the same lens. For example, the light field observed at the second slit position is the Fourier transform of the light field transmitted by the second VIPA. When the second slit is fully open, the light field observed at the diffraction mask position is identical to the light field transmitted by the second VIPA (conjugate planes). This is illustrated in Figure 3A, which shows a numerical simulation of the Rayleigh light field component observed at the diffraction mask position when both slits are fully open. It shows a series of intense spots arranged in an almost square grid corresponding to the product of the two VIPA transmissions. Note that in this case, the Brillouin light field shows a very similar pattern (not shown). Consequently, designing a mask to improve the contrast of the spectrometer under these conditions will come at a significant cost to the Brillouin intensity when placed in either of these two planes.

<figure><img src="image_4.png" /><figcaption>Figure 3: Simulation of the light field at the diffraction mask position, A) Rayleigh component, no slit. The patterns for the Stokes and anti-Stokes Brillouin components are similar; B) Rayleigh component, slits partially closed to block all the Rayleigh peaks; C) Stokes Brillouin component, slits partially closed to cut all the Rayleigh peaks. The pattern for the anti-Stokes component is similar. The red line in B and C shows the edge of the diffraction mask, leaving the upper right quadrant unaffected.</figcaption></figure>

However, the Rayleigh light field component calculated at the diffraction mask position is significantly modified when the slits are partially closed to block the Rayleigh peaks, as shown in Figure 3B. Indeed, the remaining Rayleigh component shows a sharp peak near the optical axis, with decaying secondary maxima located symmetrically in the horizontal and vertical directions. This pattern can be understood as follows: after the second slit, all Rayleigh peaks
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have been suppressed. The remaining Rayleigh component is a nearly symmetric upward curved background given by the truncated 2D Airy function. If this were a constant electric field, the diffraction pattern would be the classical pattern of the diffraction by a square aperture, i.e. the product of two orthogonal cardinal sine functions. The diffraction pattern shown in Figure 3B is similar, although the exact shape of the peak must be different. However, the periodicity of the secondary maxima is still related to the aperture size. It can also be observed that the main peak does not lie exactly on the optical axis. This is related to the asymmetry of the complex electric field at the output of the second slit. In contrast, the remaining Stokes-Brillouin light field also calculated at the diffraction mask position is essentially only slightly blurred, as can be seen in Figure 3C. The blurring is due to the blocking of all but one of the Stokes Brillouin peaks. A similar picture is obtained for the anti-Stokes Brillouin component (not shown). Comparing Figures 3B and 3C, the Brillouin and the Rayleigh components are now well separated at the diffraction mask position when the slits are partially closed to block all the Rayleigh peaks. An L-shaped diffraction mask consisting of two perpendicular slits positioned as shown by the red lines in Figures 3B and 3C can be used to efficiently eliminate the intense central Rayleigh peak, the main secondary maxima in both directions and the uninteresting light in three quadrants without significantly reducing the intensity of the Brillouin component, as expected from Figure 3C.

The Brillouin spectra calculated at the detector position and corresponding to the different cases discussed above are shown in Figure 4. With the slits fully open (blue dashed line) and no diffraction mask, the Brillouin spectrum is dominated by the two intense Rayleigh peaks that define the free spectral range of the interferometer, with a strong background in between due to the squared Airy shape of the transmission function. The contrast of the simulated two-stage VIPA-based spectrometers is about 61 dB, slightly higher than the typically measured contrast of similar real instruments. Against this intense background, the two tiny Brillouin peaks are barely visible because they have been introduced with an intensity factor of 10⁻⁶ compared to the Rayleigh component to mimic the reality of the physical process of Brillouin scattering. With the slits partially closed (red dashed dotted line), the Rayleigh peaks are eliminated, but the background associated with the limited contrast remains fully intact, still masking the Brillouin signal. Finally, positioning the diffraction mask as shown in Figure 3B eliminates much of the background, revealing the two Brillouin peaks with almost no loss in intensity (yellow solid line). The contrast is now about 86 dB, or a theoretical gain of 25 dB for about 89% transmission (-0.5 dB) of the Stokes-Brillouin component.
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<figure><img src="image_5.png" /><figcaption>Figure 4: Simulation of the Brillouin spectra obtained in the image focal plane of SL4, at the (detector position, with no slit (blue dashed line), slits partially closed (red dashed dotted line), slits partially closed and diffraction mask in place (orange solid line) as shown in Figure 3B.</figcaption></figure>

**6. Diffraction mask experimental testing**

The used diffraction mask is a rectangular aperture consisting of four independent knife-edge blades (Rectangular Aperture, Ealing), though only two perpendicular blades are typically used. For Fig. 2C, these would be the vertical left blade and the horizontal lower blade. Note that the useful quadrant changes depending on how the two VIPAs are oriented. Since this optomechanical component lacks micrometer drives with fine pitch, it is mounted on a manual XZ linear translation stage (TSD-404SL, OptoSigma) which provides 6.5 mm of travel for precise adjustment of the mask's position. With a maximum aperture of 12 mm, the mask can be inserted into the optical path without blocking the signal. When the slits are fully open, the Rayleigh light field component is indeed easily observable with a piece of paper placed just after the mask. With the slits properly closed, one of the two useful blades of the rectangular aperture is slowly closed until the intense background visible on the CCD suddenly decreases drastically. Then, the blade is opened slightly just to reveal the background again. The same procedure is repeated with the perpendicular blade. To optimize the diffraction mask's efficiency, — that is, to achieve high contrast gain and high transmission of the Brillouin components — the rectangular aperture is then precisely translated in the two perpendicular directions using the micrometer drives while observing the effects on the CCD.
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To test the efficiency of the proposed diffraction mask, a series of Brillouin spectra were acquired across a water/polystyrene interface using a Nikon 60x water immersion objective (NA=1) and a polystyrene petri dish. The power of the incident laser beam at the exit of the objective was 5.8 mW. With this objective, the radius of the laser spot is ~0.25 µm (1/e² value) so a pinhole with a diameter of 100 µm was used according to the optical magnification. Figure 5A to 5C (upper raw) shows the raw images obtained respectively at three different Z values, 20 µm, 6 µm and 0 µm above the surface without the diffraction mask. The intensity scale is the same for all raw images, 0 for dark blue and 500 counts for yellow. The background increases by a factor of about 15 from C₁ to C₂ and by a factor of about 400 from C₁ to C₃. The Brillouin component at 20 µm above the interface is already on a significant background, mainly due to the intense Rayleigh scattering caused by the specular reflection. Figure 5G shows the evolution of the Brillouin Stokes (solid lines) and the background (dashed lines) intensities as a function of the distance from the water/polystyrene interface. The reported background intensity is the values of the background at the frequency of the Brillouin peak. When the diffraction mask is not in place (blue lines), the Brillouin component at 20 µm above the interface is already on a significant background. The corresponding Brillouin spectrum is plotted in Figure 5H (blue dots) together with a fit of the sum of a Lorentzian, modeling the Brillouin peak, and a linear function, modeling the tail of the Rayleigh peak, to the experimental data. As the distance to the interface decreases, the background rapidly increases and dominates the Brillouin intensity below 10 µm, precluding its observation, see Figures 5B and 5C.
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<figure><img src="image_6.png" /><figcaption>Figure 5: A-F) Raw data obtained at three different Z values, 20 µm, 6 µm and 0 µm above the surface (from left to right); without the diffraction mask (upper raw) and with the diffraction mask (lower raw). Note that the intensity scale is the same for all images, 0 for dark blue and 500 counts for yellow. The background increases by a factor of about 15 from C₁ to C₂ and by a factor of about 27 from C₂ to C₃. The signal appearing at the center of the lower raw images is the polystyrene Brillouin doublet. G) Brillouin (solid lines) and background (dashed lines) intensities measured across the water/polystyrene interface with (red) and without the diffraction mask (blue). Negative Z-values indicate a position in water. H) Brillouin spectra obtained 20 µm above the interface with and without the diffraction mask. The solid line is a Lorentzian fit of the experimental data points.</figcaption></figure>
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With the diffraction mask placed as shown in Figure 3B, the background intensity drops to a negligible value when the laser beam is focused at least 5 µm above the interface (Figure 5G, red dashed line), see also Figure 5D and Figure 5E. In this region, the Brillouin intensity is essentially constant (Figure 5G, red solid line) and signal-to-noise ratio of the Brillouin spectrum is high, as shown in Figure 5H (red dots). Below 5 µm, the background intensity begins to increase as the distance from the interface decreases. However, when the laser beam is focused on the interface at Z = 0, the maximum background intensity is still five times smaller than the Brillouin intensity. Thanks to the diffraction mask, the Brillouin spectrum can be easily observed very close to the interface, see Figure 5F. Below the interface, the Brillouin peak of water can still be observed due to the limited axial resolution (~0.55 µm, 1/e² value) accompanied by an increase in intensity of the polystyrene Brillouin doublet around 13-17 GHz. An increase in contrast of 27 dB can be estimated from the ratio of the background intensity values at Z = 0 between the measurements with and without the mask. Note that this increase in contrast, measured at the Brillouin peak position, is slightly higher than the value obtained from the numerical simulation measured at the center of the Brillouin spectrum. This is probably due to the position of the diffraction mask which was probably slightly more closed than in the case shown in Figure 3B. The transmission of the Brillouin component is indeed slightly lower, ~85%, than that obtained by the simulation.

## 7. Brillouin mapping

The spectrometer described above was then applied to adult human dental pulp stem cells (hDPSCs). These cells were isolated from third molar germs extracted during dental treatment at the University Hospital of Montpellier with the patient's consent "Comité de protection des Personnes Sud Mediterrannée IV, Centre Hospitalier de Montpellier, process n° 2014-2198". The cells were then cultured in a T75 flask with complete culture medium: Alpha-MEM with 1% penicillin-streptomycin and 10% fetal bovine serum (FBS). They were then incubated at 37°C under 5% CO₂ until they reached 80% confluence, the term used to describe the ratio between the space occupied by the cells and the total space of the substrate. They were then detached with trypsin/EDTA for 2 to 5 minutes in an incubator at 37°C and 5% CO₂. Finally, they were fixed with 4% paraformaldehyde solution for 15 minutes and then washed three times with PBS. Fixation allows the tissue to be preserved for long periods of time without degradation.
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Human dental pulp stem cells are transparent and relatively flat, with a thickness of only a few microns. To limit the intensity of the specular reflection in the backscattering configuration using the Nikon 60x water immersion objective, 300 cells were cultured and fixed on a 1" MgF2 plate (WG61050, Thorlabs). In fact, the refractive index of this crystalline material is much closer to that of water than to that of polystyrene, the standard material used for most cell culture dishes in biology. At a wavelength of 532 nm, the refractive indices of water, polystyrene and MgF2 are 1.3354, 1.5983 and 1.3789, respectively, resulting in specular reflection intensities of approximately 0.8% for the water/polystyrene interface and only 0.026% for the water/MgF2 interface. Using a MgF2 substrate instead of the classical polystyrene reduces the specular reflection by 15 dB. This is a significant gain that can be essential for certain experiments, especially in the backscattering configuration. In other words, an experiment that would require a Brillouin spectrometer characterized by a contrast of 95 ~dB would be successful using our spectrometer and a MgF2 plate instead of polystyrene. Note that this significant reduction in specular reflection using a MgF2 substrate is only effective for transparent materials. A second interest of using a MgF2 plate is that the Brillouin Stokes and Anti-Stokes peaks resulting from interaction of light with this material are located at about 42 GHz for an incident wavelength of 532 nm, far from the usual Brillouin shifts observed for biomaterials compared to polystyrene, and much less intense.

<figure><img src="image_7.png" /><figcaption>Figure 6: High-resolution images of a hDPS cell reconstructed from the Brillouin frequency shift (A), the Brillouin peak intensity (B) and the full width at half maximum (FWHM) (C). Scale bar 2 mm.</figcaption></figure>
A high-resolution spatial Brillouin mapping of a hDPS cell was obtained in about 1 hour using 0.2 µm steps, slightly smaller than the radius of the laser spot. The power of the incident laser beam at the exit of the objective was 5.8 mW. The image is composed of 11476 Brillouin spectra each acquired with an exposure time of 300 ms. At the beginning and after each scanned line, the laser beam position is shifted back to the (0,0) position in the water to acquire a reference spectrum. The latter is used to compensate for the small drift of the Brillouin spectra measured on the camera due to the slow wavelength drift of the laser with time. An image reconstructed from the measured Brillouin frequency shifts is shown in Figure 6A. The blue color corresponds to water ($v_B \approx 7.4$ GHz) while the yellow color corresponds to stiffer material. The nucleus and organelles, as well as the membrane folds, are distinguishable despite their thinness. The separation between the external environment and the cytoplasm, the internal fluid of the cell, is also visible. The measured intensity of the Brillouin peaks is also influenced by the nature of the material, as shown in Figure 6B. The region where the Brillouin shift is significantly higher than that of water is characterized by a lower Brillouin intensity. Along the same line, the Brillouin peaks in this region are also broader, as observed in Figure 6C.

<figure><img src="image_8.png" /><figcaption>Figure 7: (A) optical microscope image of porcine dentin. (B) High-resolution image reconstructed from Brillouin frequency shift showing tubules and canaliculi. Scale bar 5 µm.</figcaption></figure>

To further demonstrate the capabilities of our Brillouin spectrometer we attempted and succeeded in obtaining similar Brillouin images in the case of the much less transparent porcine
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dentin mineralized material. A 40x40 µm² high-resolution spatial Brillouin mapping was obtained in about 1.5 hours using 0.3 µm steps. The image is composed of 17956 Brillouin spectra each acquired with an exposure time of 300 ms. The power of the incident laser beam at the exit of the objective was 5.8 mW. An image reconstructed from the measured Brillouin frequency shifts is shown in Figure 7B. The mechanical properties of the peritubular regions, characterized by the highest Brillouin frequency shifts around 20 GHz, differ significantly from those of the intertubular regions, characterized by the lowest Brillouin frequency shifts around 18.5 GHz. Interestingly, the Brillouin image also reveals the mechanical inhomogeneity of the latter regions where canaliculi characterized by slightly higher Brillouin frequency shifts form a tangle of tubules. The latter are not visible in the optical image shown in Figure 7A. Further details can be found in Younes et al. [51].

## 8. Discussion

The significant contrast enhancement we observed when placing our L-shaped diffraction mask is related to that previously described by E. Edrei et al. [31]. However, we have enhanced the filtering of the Rayleigh contribution while maintaining significant transmission of the Brillouin signals by accounting for the symmetry of the electric field generated by the crossed VIPA. To understand the main difference between our proposal and the findings reported by Edrei et al. let us first summarized this paper. The authors observed that the situation encountered in VIPA-based Brillouin spectrometers is comparable, but opposite, to that faced by coronagraphic telescopes to image, for example, a faint companion close to a brilliant star [52]. In this analogy, the circular Lyot mask blocking the intense starlight is replaced by the two slits cutting the Rayleigh peaks. The remaining signal in the coronagraph, including the star's Airy rings and the companion light, is replaced in the VIPA-based Brillouin spectrometer by a background resulting from the truncated 2D Airy transmission of the crossed VIPAs and the two Brillouin components. In the case of the coronagraph, the projected image of the starlight shows a corona that can be masked by a slightly undersized circular aperture, the Lyot stop. Its counterpart in the VIPA-based Brillouin spectrometer would then be a small blocking disk that would stop the intense central peak of the diffraction pattern. Our calculations show that the background on the detector remains important with such a mask. This is partly due to the specific diffraction pattern of the truncated transmission function of the crossed VIPA, whose main peak contains only about 46% of the total energy, instead of about 84% for the classical circular aperture. In addition, the remaining Rayleigh intensity spectrum shows rather
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strong oscillations whose spatial period decreases with the mask size, which would probably complicate data analysis and increase errors.

This is the limit of the simple analogy with the classical coronagraph telescope, and we propose in this article a diffraction mask more specific to the electric field generated by the crossed VIPA transmission and the partially closed slits. The latter has a quadratic symmetry and occupies only one quadrant, so it seems appropriate to use an L-shaped diffraction mask, as discussed earlier. Placed as shown in Figure 3C, the mask has a transmission of 3% of the Rayleigh component, corresponding to a 15 dB suppression and an average transmission of over 85% of the Brillouin components. In this case, the shape of the diffracted Rayleigh background remains a monotonous upward curve around the Brillouin peaks, and a significant portion of the Rayleigh component is rejected outside the region of interest as shown in Figure 4, explaining the final 25 dB increase in contrast in the center of the Brillouin spectrum. Thus, with this L-shaped diffraction mask it is not necessary to further apodize the output field of the VIPA etalons to achieve a total contrast of 80 dB, which would also reduce the transmission of the Brillouin signal. Furthermore, simulations show that such apodization significantly reduces the efficiency of a diffraction mask, since the intense central Rayleigh peak observed in Figure 3B is replaced by a dozen peaks that largely cover the spatial region where the Brillouin signal is strong.

## 9. Conclusion

In this work, we extended the analogy with the negative coronagraph originally proposed by E. Edrei and G. Scarcelli. We successfully designed a simple, efficient diffraction mask that is optimized for the electric field transmitted by the crossed VIPA etalons and partially closed slits. To demonstrate its efficiency, we measured the Brillouin spectrum of water across the interface of a polystyrene dish. Using the diffraction mask, we achieved a remarkable 27 dB increase in contrast while maintaining 85% of the Brillouin signal. Even when the laser beam is focused on the interface, the maximum background intensity remains five times smaller than the Brillouin intensity. The magnitude of the contrast increase is in very good agreement with numerical simulations of the light field propagation across the spectrometer using the standard angular spectrum method. This suggests that this method is promising for optimizing such Brillouin spectrometers. Furthermore, the L-shaped diffraction mask is easily implemented in our VIPA-based confocal micro-Brillouin spectrometer using a commercially available rectangular aperture consisting of four independent knife-edge blades. Our ability to obtain a
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high-resolution, one-hour Brillouin mapping very close to an interface demonstrates the high stability of the setup including the L-shaped diffraction mask. The successful large-scale mapping of the much less transparent material porcine dentin material confirms the high contrast and high intensity throughput of the spectrometer. Additionally, the diffraction mask design is compatible with single-stage VIPA-based Brillouin spectrometers. Due to its simplicity, we expect this new mask to find wide application in VIPA-based spectrometers to achieve contrast above 80 dB.

### Acknowledgment

Study has been realized in EDMOS platform created with the financial support of the Region Occitanie (France) and the European Regional Development Fund (ERDF).

### Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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