Single-pixel diffuser camera

A simple proof-of-concept experimental realization of the approach is presented in Figure 2. Figure 2 (a) depicts the optical configuration of a single-color SP-DiffuserCam, where the light source is a monochromatic 530 nm LED with a bandwidth of 33 nm (M530D2, Thorlabs). The object is imaged on the diffuser plane, illuminated by the collimated light. The ground glass diffuser ($\varnothing$ = 24mm, DG10-120-MD, Thorlabs) is mounted on a motorized rotation stage (PRM1/MZ8, Thorlabs), which has a 25 ^∘/second rotation velocity. A silicon amplified photodetector (PDA100A2, Thorlabs) is used to measure the intensity fluctuations. For calibration, the speckle patterns $P(x,y,\theta)$ of the diffuser are recorded by a camera (panda 4.2 bi, PCO AG) through the same lens (f=50mm) used for the photodetector to keep the same numerical aperture; the exposure time of 4ms is the same for both detectors. A motor controller (KDC101, Thorlabs) and a low-cost DAQ device (USB-6002, National Instruments) are used to synchronize the rotator and the detector or the camera.

To ensure our patterns are sufficiently different, we use the edge of the diffuser region(about $d=6mm$ from the center of the diffuser) as the image plane area. Due to the small diameter of the diffuser, however, the neighbouring patterns still have similar areas along the rotation direction. The objects (Figure 2(b) left) are 3D printed transmission masks of ’U’, ’T’, ’S’ with a thickness of 2mm and the size about 3mm. The retrieved $64\times 64$ pixel images with sampling ratios of 2.2%, 4.4%, and 8.8% are shown in Figure 2(b), corresponding to a minimum acquisition time of 14.4s, which is limited by the maximum rotation velocity. Here we also use a simple block-matching and the collaborative filtering algorithm [22] for noise suppression, which takes about 0.02 seconds. Outlines of objects emerge at 2.2%, with image quality increasing with improved sampling ratios to 8.8%. Further increasing the number of scattering patterns would not improve the reconstruction quality. The first reason is the ’imperfect’ reference patterns with overlap regions between neighbouring ones. The second one is that a higher sampling ratio leads to a finer angle variation of measurement within one cycle of rotation, and increased overlap areas of the reference patterns. Thus, the above challenges induce a phenomenon that the spatial information along the vertical direction of rotation is reconstructed better than the parallel ones. This is evident in Figure 2(b), in the top-right corner of ’U’, the bottom of ’T’ and the emerging noisy pixels in the left of ’S’. Note the rotation directions are clockwise the three masks, with the sampling area in the lower half of the circular diffuser.

The performance of our setup is largely dependent on the choice of diffuser. Here we compare the 120-grit diffuser, which is used in Figure 2, and a 220-grit diffuser ($\varnothing$ = 24mm, DG10-220-MD, Thorlabs), which has smaller grain size on the polished surface. Figure 3(a) shows typical transmission images of the two diffusers, in which the former one shows a higher contrast than the later one, due to the coarser polishing. We calculate the correlation coefficient $C(I_{\theta 1},I_{\theta 2})$ of the two groups of diffuser patterns, for a quantitative study, as defined by

where $\theta$ = 0^∘,1^∘,$\cdots$, 360^∘, $\bar{I}_{\theta 1}$ and $\bar{I}_{\theta 2}$ denote the average values for two arbitrary patterns $I_{\theta 1}$ and $I_{\theta 2}$, respectively. The mean correlation coefficients between different angles for the 120 grit diffuser is $C(I_{120})=0.55$, while for the 220 grit one we find $C(I_{220})=0.87$. Note that these coefficients are based on $1024\times 1024$ pixels reference patterns, and they would be further higher in the condition of Figure 3(b), where the patterns are binned to $64\times 64$ matrices with lower contrasts. A higher correlation means an improved intrinsic coherence between the sampling basis and leads to a lower detection efficiency of the spatial images. Key to contemporary single-pixel imaging is the use of high-efficiency orthonormal patterns, such as Hadamard [12] or Fourier basis [7]. However, since we adopt a commercial diffuser, the sampling patterns in our setup are actually pseudo-random grayscale matrices, which are more related to classical GI using laser and dynamic diffuser induced speckle patterns [18]. According to a study of the influence of speckle size in GI [23], an optimal speckle size exists in the range where the speckle size is comparable to the feature size of the object. This is the reason that we choose to use the 120-grit diffuser, as it is our coarsest diffuser and the one most approaches the feature size of the masks (about $0.4mm$). Future work could focus on the optimization of the diffuser or an integrated mini camera.

One of the advantages of the SP-DiffuserCam is that it is easy to integrate other functions within the platform, such as the hyperspectral imaging shown in Figure 4. To do this, we can directly use the pre-recorded reference patterns without additional calibration for specific wavelengths. Figure 4 (a) illustrates the optical setup of the hyperspectral SP-DiffuserCam. Here we use a cold white LED (MCWHLP1, Thorlabs) for a broad spectrum. Different from the monochrome setup, a low-cost diffraction grating slide (1,000 Line/mm, Rainbow Symphony, $0.40), is used to disperse the incident light. The object image on the diffuser passes through the grating after the imaging lens (f=50mm) and is focused onto a line array detector via the collection lens (f=35mm). Here a compact COMS camera (acA1920-150um, Basler) serves as line-detector by binning the pixels to a $16\times 1$ array in a sensor area of $9.5mm\times 3.3mm$. To keep the same numerical aperture with the single-pixel measurement, we use the same two lenses system for calibration.

The 1D spectral intensity at each degree (exposure time: 4ms) are recorded in a 2D matrix $I(\theta,\lambda)$. Then this matrix is converted to a spectral data cube $R(x,y,\lambda)$ by the reconstruction Equation 3. Here we apply standardized [International Commission on Illumination (CIE)] color-matching functions to the spectral cube to produce the pseudo-colored images to make consistent with the original object (made by sticking the color filters to the ’T’ mask, a blue filter for the ’-’ and a red filter for the ’$|$’ of ’T’). Figure 4 (b) shows the retrieved spectral image in the blue band ($461\pm 35nm$) and the red band ($627\pm 10nm$). Compared with the object photograph in the lower right corner, the middle, overlap area in the reconstruction has much lower intensities, due to refraction between the junction of the two filters. The reconstructed spectra of two selected areas in Figure 4 (b) show a similar trend when compared to measurements using a conventional spectrometer (UV-2401 PC UV-VIS, Shimadzu) of the same two color filters. Finally, we show the 3D spatio-spectral data cube in Figure 4 (d), as well as the spatial mapping image at single wavebands ranging from 426nm to 637 nm.