Deep Contrast and Companion Detection Using the EvWaCo Testbed Equipped with an Achromatic Focal Plane Mask and an Adjustable Inner Working Angle

Figure 1 shows an illustration of the current EvWaCo testbed. The setup comprises two sources: the star source and the companion source. The star source is made of a stable tungsten lamp that emits a collimated beam and is focused by an achromatic doublet lens on a 50 $\micron$ multi-mode fiber. This multi-mode fiber is connected to a single mode fiber that directs the light toward the coronagraph bench.

The companion source comprises an LED that emits a beam at the central wavelength $\lambda_{c}$ = 780 nm with a spectral bandwidth of $\Delta\lambda/\lambda\approx$ 3%. The light emitted by this LED is injected into a single mode fiber. The beams emitted by the star and the companion fibers are recombined by a beamsplitter BS, collimated by the lens L1 and transmitted through the aperture stop AS of diameter $D_{AS}$. The beam transmitted by the AS is focused by the lens L2 on the Focal Plane Mask (FPM). The on-axis beam incident on the FPM is transmitted while the off-axis beam is reflected by the mask and directed towards the collimating lens L3 and the Lyot Stop LS. The beam transmitted by the LS is focused by the lens L4 and directed by a folding mirror towards the CCD camera. This CCD camera is mounted on a translation stage for fine focusing. A photometric filter, which can either be I-band or R-band, is placed in front of the CCD.

A filter wheel, placed in front of the camera, houses a neutral density filter OD2 for measuring the unsaturated PSF peak and an achromatic doublet to re-image the pupil plane on the camera. The camera used is an FLI Interline CCD camera cooled at temperature T = -14.6^∘ C with a pixel size of 7.4 µm. During the contrast measurements, all the optical components after the lens L2 are enclosed in a black box to protect from stray light.

Figure 2 shows the spectral flux incident on the detector. It takes into account the irradiance due to the tungsten halogen lamp, single mode fiber, transmission coating of the achromatic doublets and the prism used. The relative spectral ratio is approximately equal to 20% in the I-band and 23% in the R-band.

The current EvWaCo testbed has been upgraded with a new coronagraphic mask built according to the design presented in Figure 3. The static prism S is mounted on the static support while the translating prism is mounted on the carrier moving along the high precision linear slide. The pressure between the lens and the prism is adjusted by turning the micrometer which compresses a coil spring put in contact with the lens. The force over the contact area can be controlled from 0 N to 50 N with an accuracy equal to 0.02 N. We emphasize that the support of the static prism has been designed in order to keep the line of sight stable while adjusting the pressure between S and T with an accuracy better than 15”.

This coronagraphic mask is mounted on a support (Figure 4-left) that comprises five degrees of freedom: two translations in the horizontal plane, one rotation around the vertical axis and two rotations around the horizontal axes. The tip-tilt orientation of the mask can be adjusted over a range larger than +/- 5 degrees and with an accuracy better than 10”. This tip-tilt mount is mounted on two translating stages each equipped with a micrometer which is used to position the focal plane mask on the focus with an accuracy equal to 2 µm. Figure 4 (right) shows a close-up view of the coronagraphic mask.

Figure 5 represents the variation of the shape of the coronagraphic mask for a force applying S on P, and varying from 0.10 N and 10.5 N for a source of central wavelength $\lambda_{1}$ = 800 nm with a Full Width at Half Maximum (FWHM) of 40 nm. At the time of these measurements, the reference is considered to be the case where the lens and the prism are placed in contact without applying any force.

There is no force sensor in the setup so the force is calculated using the configuration of a sphere place in contact with a flat plate (Hertzian contact stress) (Budynas, Nisbett, 2014). We calculate the contact stress (diameter of the hole) that corresponds to a specific contact pressure represented by the micrometer readings. This results to a force profile given the actuator reading, and thus, relate the diameter of the contact area to the force/pressure applied. Figure 5 also shows the x- and y- profiles of the mask response to increasing pressure. It can be observed that as pressure on the prism increases, the size of mask increases in terms of the FWHM and the contact area.

In this paper, the inner working angle (IWA) is defined as the distance from the star center where the post-coronagraphic throughput is 50%. Thus, it is expressed in terms of $\lambda/D$ where D is the diameter of the aperture stop. Since the size of the mask directly impacts the IWA, by varying the force applied by the lens on the prism, the IWA can be finely tuned as well. For example, an FWHM of 222 µm corresponds to 3.7 $\lambda/D$ at $\lambda_{c}\approx$ 800 nm.

The pressure of the lens has been adjusted until an IWA approximately equal to $3\lambda_{1}/D$ is achieved along the minor axis for a source central wavelength equal to $\lambda_{1}\approx$ 800 nm. All the experiments presented hereafter have been performed under this pressure unless specified otherwise.

To model this coronagraphic mask, the air thickness, d, is approximated by a polynomial equation given by Equation 1:

where $a_{1}$ and $a_{2}$ are the coefficients of the polynomial of degrees 1 and 2, respectively, and $\rho$ is the radial distance to the contact point in the prism hypotenuse plane. We calculate the theoeretical reflection coefficients by applying the coefficients locally in the case of thin, homogenous air gap with an optical index, $n_{2}$, sandwiched between two optical indices, $n_{1}$, and $n_{3}$ (Buisset et al., 2017; Zhu et al., 1986). The coefficients of the polynomial are calculated by minimizing the sum of the squared difference between the simulation and the experimental data. We use a built-in function in Matlab called fminsearch that uses the Nelder-Mead simplex direct search (Lagarias et. al., 1998) to perform the optimization. Using this optimization, the coefficients of the polynomial are found to be $a_{1}=-1.10^{-3}$ and $a_{2}$ = 36 $\micron^{-1}$.

Figure 6 compares the theoretical and the experimental mask reflectivity for unpolarized light. The extracted profiles from the experimental data are normalized with respect to the median value of the calibrated image that is measured at a distance equal to 400 µm (13 $\lambda_{1}/D$) from the optical axis of the coronagraphic mask. The horizontal error bars represent $\pm$ 1 pixel while the vertical error bars represent the standard deviation $\pm\sigma$ of 101 intensity measurements.

The mask profiles show that the FWHMs along X and Y are $FWHM_{x}$ $\approx$ 240 µm and $FWHM_{y}$ $\approx$ 180 µm, respectively. Consequently, the measured IWAs are as follows: $IWA_{x}$ $\approx$ 4.00 $\lambda_{1}/D$ and $IWA_{y}$ $\approx$ 3.00 $\lambda_{1}/D$ at the wavelength $\lambda_{c}$ = 800 nm.

This enlargement of the mask along the X axis is due to the angle of incidence on the coronagraphic mask prism hypotenuse as discussed in our previous paper (Buisset et al. 2017). We verified that the ratio $IWA_{x}/IWA_{y}=1/cos(\theta)$ is equal to 1.33 that is compatible with an angle of incidence approximately equal to $\theta=41.4^{\circ}$.

At distances comprised between -50 µm and +50 µm along the x-axis and between -30 µm and +30 µm along the y-axis, we notice that the theoretical mask transmission is slightly smaller than the experimental one. This difference is close to the error bar but could explain the discrepancy between the theoretical and the experimental raw contrasts at distances smaller than 3 $\lambda/D$ as presented in Section 5 and in Figure 10.

At distances comprised between +50 µm and +150 µm along the x-axis and between +70 µm and +125 µm along the y-axis, we notice a good match between the theoretical model and the experimental results, and the FWHM is correctly modelled. At distances greater than 150 µm in the x-axis and 120 µm in the y-axis, we notice a slight discrepancy between the theory and the experimentation. However, at these distances, we expect that this small difference will only have a small impact on the raw contrast calculation.

We, then, investigate the response of the new focal plane mask to a different wavelength, $\lambda_{2}$ = 650 nm. To measure the mask response at $\lambda_{2}$, we used an LED emitting at $\lambda_{peak}$ = 617 nm and a spectral filter centered at $\lambda_{2}$ = 650 nm with an FWHM equal to 40 nm.

Figure 7 shows the theoretical and experimental mask response profiles of the focal plane mask obtained using the spectral filter with central wavelength, $\lambda_{2}$, and compared it to the mask response at $\lambda_{1}$. The theoretical mask response is calculated by using the same polynomial coefficients obtained at 800 nm. We observe that the mask profiles are smaller at $\lambda_{2}$ (blue curve) compared to the ones obtained at $\lambda_{1}$ (pink curve). In terms of the IWA, the values are quite close. At $\lambda_{2}$, $IWA_{X}\approx$ $4.27$ $\lambda/D$ ($FWHM_{X}\approx$ $208$ µm) and $IWA_{Y}\approx$ $3.24$ $\lambda/D$ ($FWHM_{Y}\approx$ $158$ µm).

These results show that the mask itself adapts well to the wavelengths between $\lambda_{1}$ and $\lambda_{2}$ that correspond to the central wavelengths of the I- and R- bands of the Johnson-Cousins photometric filter. These first experimental observations of the quasi-achromatic behavior of the mask confirms the theoretical prediction for two wavelengths separated by 150 nm.

Figure 8 represents the irradiance distribution at the exit pupil plane when the PSF of the star source is placed off-axis (left) and when it is centered on the mask (right). These images were obtained by placing a lens, L5, inside the filter wheel (see Figure 1) in order to image the exit pupil. The LS diameter is equal to 81% of the exit pupil diameter and transmits approximately 65% of the incident light. The results show that the energy is mostly concentrated at the edges, forming a fine annular shape with a diameter that is approximately 2 mm, and an average extension width equal to 86 µm.

Figure 9 illustrates the calculation of contrast adapted in this paper. We decided to take the definition of the raw contrast presented in (Ruane et. al, 2018). Thus, the raw contrast is calculated as:

where $\eta_{s}(x_{o},\lambda)$ is the fraction of available starlight detected and $\eta_{p}(x_{o},\lambda)$ is the fraction of companion light detected. The quantity $\eta_{s}(x_{o},\lambda)$ is given by

where $PSF_{coro}(x,0,\lambda)$ is the point spread function (PSF) centered on the focal plane mask recorded at the image plane and AP($x_{o}$) is equal to 1 pixel. Meanwhile, the quantity $\eta_{p}(x_{o},\lambda)$ is calculated as

where $PSF_{coro}(x,x_{o},\lambda)$ is the PSF recorded at a distance $x_{o}$ from the center of the mask. We assume that $PSF_{coro}$ is invariant over the FOV of the coronagraph at distances higher than 7 $\lambda/D$ where the mask transmission is close to 1.

In Figure 9 (left), we show an image of the star residual irradiance $PSF_{coro}(x,0,\lambda)$ and the PSF of the companion $PSF_{coro}(x,x_{o},\lambda)$ measured at a distance $x_{o}=$ 8 $\lambda/D$ from the mask center. On the right, we illustrate the calculation of $\eta_{s}$ and $\eta_{p}$ from the cross-section of the $PSF_{coro}(x,0,\lambda)$ and $PSF_{coro}(x,x_{o},\lambda)$, respectively.

In our case, the fraction of the available starlight is the normalized irradiance, $I_{norm}$, that is the ratio between the unsaturated off-axis PSF peak and the on-axis PSF. Discussion on the calculation of $I_{norm}$ from the experimental data can be found in the Appendix. The light detected from the companion, on the other hand, depends on the transmission, $T(x,\lambda)$, of the mask. The raw contrast is, then, calculated as

We show in Figure 10 the normalized irradiance and raw contrast obtained using two spectral bands of the Johnson-Cousins photometric filter (Bessel et al., 1990): I-band and the R-band. The I-band filter has a central wavelength $\lambda_{c}$ = 800 nm with a wavelength range between 700 nm and 900 nm and a spectral ratio $\Delta\lambda/\lambda_{C}$ = 20%. Meanwhile, the R-band filter has a central wavelength of $\lambda_{c}$ = 650 nm with a wavelength range between 550 nm and 800 nm and a spectral ratio $\Delta\lambda/\lambda_{C}$ = 23%. We note that only the bandpass filter located in front of the camera during the acquisitions over the full I-band or the R-band is changed.

We superimpose on the same figure the results of the simulations done using the same model described in (Buisset et al., 2018) represented by the dashed lines with an updated mask transmission. This model takes the following inputs: i) spectral flux incident on the detector (see Figure 2), ii) the air thickness profile (see Figure 6), iii) the diameter of the AS and LS, and iv) the focal length of L2, L3 and L4. The complex amplitude incident on the FPM is obtained by taking the Fourier transform of the complex amplitude transmitted by the AS while the complex amplitude incident on the CCD is obtained by taking the Fourier transform transmitted by the LS. A full description of this model can be found in (Buisset et al., 2018).

Figure 10 shows the radial average of the raw contrast measured at radial distances between 1.5 $\lambda/D$ to 20 $\lambda/D$ (pink curve). We superimpose in the same graph the mask response curves obtained through the experiment and simulations. For both spectral bands, the coronagraph reduce the PSF peak by three orders of magnitude.

Between 3 $\lambda/D$ and 4 $\lambda/D$, the raw contrast in the I-band varies between $2.10^{-4}$ and $5.10^{-5}$ while it varies between $2.10^{-3}$ and $3.10^{-4}$ in the R-band. Meanwhile, along the same distance, the theoretical raw contrast varies between $1.10^{-3}$ and $2.10^{-4}$ in the I-band and between $3.10^{-3}$ and $2.10^{-4}$ in the R-band. Between 4 $\lambda/D$ and 5 $\lambda/D$, the raw contrast in the I-band varies between $5.10^{-5}$ and $2.10^{-5}$ while it varies between $3.10^{-4}$ and $8.10^{-5}$ in the R-band. On the other hand, the theoretical raw contrast at the same distance varies between $1.10^{-4}$ and $3.10^{-5}$ in the I-band and between $2.10^{-4}$ and $4.10^{-5}$ in the R-band. We, thus, notice a difference between the theoretical model and the experimental data. The potential origin of this discrepancy could be to the mismatch between the theoretical and the experimental mask transmission as discussed in the previous section. Although the experimental raw contrast values between the two bandpass differs by an order of a magnitude, the theoretical results show that the raw contrast performance is similar in the R- and I-bands, thus, confirming the theoretical achromaticity of EvWaCo. We suspect that the presence of low-order aberrations close to the IWA contributed to the discrepancy in the experimental raw contrast value.

Between 5 $\lambda/D$ and 10 $\lambda/D$, the contrast decreases from C $\approx$ $2.10^{-5}$ to C $\approx$ $3.10^{-6}$ for the I-band and from C $\approx$ $8.10^{-5}$ to C $\approx$ $9.10^{-6}$ for the R-band. Along the same distance, the theoretical contrast is between C $\approx$ $10^{-5}$ to C $\approx$ $10^{-6}$ for both the I-band and the R-band. We believe that the origin of this difference between the experiment and the theoretical contrast is the presence of speckles in the experimental measurements. Overall, our theoretical results show that the similarity between the I- and R-bands is valid at every radial distance. This confirms one more time the theoretical achromatic behavior of the EvWaCo mask in unpolarized light over the two spectral bands.

Figure 11 shows the experimental raw contrast obtained at different IWA. We notice that the best raw contrast performance is always reached with the FPM with the smallest IWA. It is important to mention that :

i) The FPM transmission profile is quasi-gaussian only when the contact area is small and when the IWA is close to 3 $\lambda/D$ (minor axis). This quasi-gaussian shape has the reputation to provide a better contrast performance than the sharp-edge transmissions obtained at larger pressure (Figure 5), and

ii) The achromatic property of this coronagraph is maximum at smaller IWA. Indeed, the chromatic variation of the mask response is valid only at the distance where the mask transmission varies between 0 and 1. Hence, we deduce that masks with a small IWA will provide a quasi-gaussian response that fully adapt itself to the wavelength. The masks with a large IWA will provide a top-hat transmission that does not change with the wavelength.

During the astronomical observations, the size of the proposed FPM could thus be adjusted in order to provide:

i) A small IWA close to 3 $\lambda/D$ to reach the best contrast performance during excellent seeing conditions of star environment imaging and companion detection and characterization, and

ii) A large IWA comprised between 3 $\lambda/D$ and 8 $\lambda/D$ during bad seeing conditions to improve the low order wavefront distortion measurement by a WFS installed on the star channel (Buisset et al., 2018) and to better correct the contrast degradation induced by the turbulence.

The large IWA could also be used to suppress the halo of extended objects with an acceptable loss of contrast performance, for example, in Cosmic Origins Science observations as mentioned in Ebbets et. al. (2015).

We consider that the coronagraph is used to detect a faint companion with its PSF located in the vicinity of the star PSF that is itself set on-axis. The detection of the companion, thus, consists of extracting the companion signal from the background noise induced by the following contributors: star residual photon noise, speckle noise, stray light photon noise, detector thermal noise and readout noise. We assess the level of this background noise by calculating the standard deviation, $\sigma_{Background}$, over an annular region starting with an inner radius R1 = 2.5 $\lambda$/D and an outer radius, R2 = 3.5 $\lambda$/D. This calculation is repeated over an annular region with inner radii equal to 3.5, 4.5,…, 19.5 $\lambda$/D, and with an annular width that is always kept equal to 1 $\lambda$/D.

On Figure 12, we have represented the level of the background noise at distances comprised between 3 $\lambda$/D and 20 $\lambda$/D (black dashed curve). Between 3 $\lambda$/D and 10 $\lambda$/D from the center of the mask, the background noise varies from $\sigma_{Background}$ $\approx$ $3.10^{-5}$ to $\sigma_{Background}$ $\approx$ $10^{-6}$. At distances greater than 10 $\lambda$/D, this noise decreases from $\sigma_{Background}$ $\approx$ $10^{-6}$ to $\sigma_{Background}$ $\approx$ $10^{-7}$. The background noise comprises the detector noise, the star residual photon noise, the stray light photon noise and the speckle noise.

We place the PSF of a companion, 25,000 times fainter than the star, at a location 5.5 $\lambda$/D distance from the center of the star. Figure 12 also shows the irradiance distribution for both the star and the companion with and without the coronagraphic effect. Obviously, when the star is off-axis, the companion is barely detected in the blinding light of the star. However, once the star is centered on the coronagraphic mask, the companion becomes visible.

The detectability of the companion is verified by calculating the signal-to-noise ratio at the location of the companion. To calculate the background noise, $\sigma_{Background}$, at the location of the companion $x_{o}$, we take the standard deviation of a circle with a radius equal to 1 $\lambda$/D, centered at $x_{o}$. Figure 12 shows the residual light profiles without (left panel) and with (right panel) the companion. We estimate that at the location of the companion, the SNR is equal to 11.

When observing the environment of stars with large telescopes equipped with AO, it is critical that the PSF is properly centered on the focal plane mask; otherwise, it will contribute to the contamination of the faint companion signal (Lloyd et al., 2005). The measurement of the variation of the contrast performance is done by installing a pointing camera. A beamsplitter is installed right after the aperture stop and the beam reflected is focused by the lens L5 on a Point Grey Camera with a pixel size of 3.4 $\micron$ as shown in Figure 1.

First, the PSF is centered on the mask which serves as the reference image. Then, tilt is introduced by de-centering the PSF on the FPM. This is done by controlling the lateral alignment of the star source fiber output face. We show in Figures 15 and 16 the irradiance distribution and the respective x- and y- profiles recorded by the CCD at the companion channel. The tilt is expressed in terms $\lambda/D$ where D is equal to the diameter of the aperture stop The error bar corresponds to the standard deviation of the contrast values calculated from the 101 images obtained for each tilt.

Along the x-axis, we notice that when the tilt is smaller than $\theta_{X}<1$ $\lambda/D$, the normalized irradiance at the IWA is better than $10^{-4}$. Meanwhile, both the normalized irradiance at 5 $\lambda$/D and 6 $\lambda$/D show slight variations. At $\pm 3$ $\lambda/D$, the cross-section along the y-axis, on the other hand, shows an asymmetry in the normalized irradiance profile. This is due to the fact that the PSF position set as the reference is slightly shifted along the y-axis. Despite that, we can deduce from Figure 16 that normalized irradiance is better than $10^{-4}$ for tilt angles smaller than $\theta_{Y}<0.2$ $\lambda/D$.

The variation of the normalized irradiance due to defocus is done by translating the star source along the optical axis and measuring the normalized irradiance value. This displacement is expressed in terms of the PTV (peak-to-valley) wavefront error. The PTV wavefront error induced by each displacement is determined by making paraxial calculations using Zemax. Figure 17 (left panel) shows the wavefront error in terms of $\lambda$ PTV induced for each displacement. For each displacement, 101 images are acquired and the normalized irradiance values are calculated over a circular annulus with an extension of 1 $\lambda/D$. The standard deviation of these values calculated for the 101 images is represented as error bars. At 3 $\lambda$/D from the center of the mask, the normalized irradiance values are better than $10^{-4}$ for a wavefront less than 0.65 $\lambda$ PTV as shown in Figure 17 (right panel).

The purpose of the Lyot stop is to reduce, if not eliminate, the residual starlight in the exit pupil plane that is due to diffraction. Thus, if this Lyot stop is not properly centered, it causes the star light to leak, thus, degrading the performance of the coronagraph. In this section, we intentionally misaligned the Lyot stop along the x- and the y-directions, and measured the normalized irradiance. Figures 18 and 19 show how the contrast varies when the Lyot stop is not exactly positioned at the center of the exit pupil (EP). The position of the Lyot stop with respect to the center of the exit pupil is marked by the black circle.

Figure 18 reveals that a misalignment of 74 µm (0.02 $D_{EP}$) along the x-direction does not significantly impact the normalized irradiance at the location of the IWA ($IWA_{X}$ $\approx$ 4.00 $\lambda/D$, $IWA_{Y}$ $\approx$ 3.00 $\lambda/D)$. The same phenomenon is observed for a misalignment of 84 µm (0.02 $D_{EP}$) along the y-direction as shown in Figure 19. These results show the possibility of enlarging the Lyot stop to 90% the size of the pupil diameter (currently, it is at 81%) at the expense of a tighter tolerance of the Lyot stop alignment.

In the experiment, we obtained two sets of off-axis PSF images, $PSF_{coro}(x,x_{o},\lambda)$, placed at a distance of $x_{o}\approx 30\lambda/D$. On the first set, we installed an optical density OD2 in front of the detector with the following transmission on each bandpass: $t_{I-band}$ = $2.10^{-3}$ and $t_{R-band}$ = $1.3.10^{-3}$. We adjusted the integration time so that the peak of the star PSF is close to the maximum dynamic range of the camera and recorded N = 101 frames of the same integration time. Then, we recorded 11 dark images and 11 bias images at an integration time equal to 1 s and 0 s, respectively. We calculated the master dark frame and the master bias frame as the median of the 11 single dark frames and 11 bias frames, respectively. We subtracted the master bias and the dark frames to each single frame of the off-axis PSF and calculated the median of the 101 images. We measured on this median image the peak value $S_{Star,peak}$ of the (unsaturated) off axis PSF.

On the second set, we removed OD2 and measured the signal $S_{Star}$ (x,y) of the PSF with the same integration time $\tau$, same number N of images and identical pre-processing method. This image of the off-axis PSF has now a saturated core but a high Signal to Noise Ratio (SNR) in the PSF wings.

To obtain $PSF_{coro}(x,0,\lambda)$, we centered the PSF on the occulting mask and recorded the signal $S_{Residual}$ (x,y) at the same integration time $\tau$. Thus, the normalized irradiance is calculated using Equation 6.

To calculate the raw contrast, we divided $I_{norm}$ by the mask transmission obtained from the experiment. For example, from Figure 10, at 3 $\lambda/D$, the normalized irradiance is approximately at $I_{norm}\approx 1.10^{-4}$ in the I-band. Thus, the corresponding raw contrast at this location is equal to $2.10^{-4}$.