Imaging Using Alternate Point Spread Functions: Lenslets with Pseudo-Random Phase Diversity

An optical imaging system’s resolution can often be limited by the detector array instead of the optics. We present alternate non-impulse like optical point spread functions that overcome the distortions introduced by the detector array. © 2005 Optical Society of America The optical point spread function (PSF) is often viewed as the resolution-limiting element of an imager [1]. For this reason conventional optical design procedures typically strive to achieve an impulse-like PSF. When such a well-designed optical system is followed by a semiconductor detector array, the resulting pixel blur and/or aliasing can become the dominant distortions present in the overall imager. In this case it is necessary to revisit the optical design. The optical PSF may now be viewed as a method of encoding the image measurement so as to better tolerate the distortions introduced by the detector array. Within such a framework we find that an impulse-like PSF can be suboptimal. Figure 1 depicts a schematic example of the problem discussed above. In figure 1a we show the image arising from a single point source in the object space of a conventional imager (i.e., one that uses an impulse-like PSF). Figure 1b shows the image of the same point object in a slightly different location. In this example we see that the large detector size (represented by the square grid) results in an identical measurement for these two object configurations and thus the resolution of this imager would be limited by the pixel spacing. Figures 1c and 1d show the analogous cases for an imager that employs an extended PSF. It is clear that given sufficient measurement SNR, simple neighborhood processing (e.g., correlation) can yield the centroid of this PSF with sub-pixel accuracy. Thus, the resolution achieved via use of an extended PSF can be superior to that of an impulse-like PSF. We consider the optical PSF to be an encoding of the object prior to measurement. The overall imaging system must therefore be viewed as “computational,” involving both the optical front end and electronic decoding [2]. The example shown in figure 1 suggests that the use of an alternate PSF can improve the condition of the decoding process, but that it may also be accompanied by an SNR cost. We will quantify this tradeoff for one simple class of alternate PSF. Our target imager design requires only modest resolution (0.1mrad) and field of view (0.1rad); however, it is characterized by an extreme form factor with an aperture of 36mm and a thickness of only 5mm. We assume the use of a detector array with 7.5μm pixels, full-well capacity of 45,000 electrons and 100% fill factor. A single-lens solution to this imager design problem is clearly not feasible and a common alternate approach utilizes a lenslet array as shown in figure 2a. Such a lenslet array will produce an array of sub-images that can be post-processed to generate a high-resolution composite image [3]. The optical PSF of this system is simply an array of diffraction-limited spots and is one example of the class of alternate PSFs described above. It is critical to insure that the lenslet CMB1 © 2005 OSA/COSI 2005