Optical Aberration Calibration and Correction of Photographic System Based on Wavefront Coding

Abstract

The image deconvolution technique can recover potential sharp images from blurred images affected by aberrations. Obtaining the point spread function (PSF) of the imaging system accurately is a prerequisite for robust deconvolution. In this paper, a computational imaging method based on wavefront coding is proposed to reconstruct the wavefront aberration of a photographic system. Firstly, a group of images affected by local aberration is obtained by applying wavefront coding on the optical system's spectral plane. Then, the PSF is recovered accurately by pupil function synthesis, and finally, the aberration-affected images are recovered by image deconvolution. After aberration correction, the image's coefficient of variation and mean relative deviation are improved by 60% and 30%, respectively, and the image can reach the limit of resolution of the sensor, as proved by the resolution test board. Meanwhile, the method's robust anti-noise capability is confirmed through simulation experiments. Through the conversion of the complexity of optical design to a post-processing algorithm, this method offers an economical and efficient strategy for obtaining high-resolution and high-quality images using a simple large-field lens.

Keywords: PSF; deconvolution; image processing; photographic system; wavefront coding.

Figure 1

(a) The experimental setup schematic. (b) The sub-aperture $M(u,v)$ loaded on the SLM. Green circles indicate the coverage of each sub-aperture. Red dots indicate the center position of the sub-aperture. Yellow arrows indicate each movement of the sub-aperture.

Figure 2

The framework of the proposed method.

Figure 3

The algorithm flow chart of the local aberration recovery process.

Figure 4

The algorithm flow chart of the pupil function reconstruction process.

Figure 5

Simulated experimental setup built in CODEV.

Figure 6

Simulation results of aberration correction: (a) original image reprinted with permission from Synopsis, Inc., (b) the line outline of the periodic line in (c). (c) The results before and after the correction of images with different noise levels are compared, and the inset boxes show the used measured PSF.

Figure 7

Experimental Setup.

Figure 8

Spatially varying aberration calibration and correction result on a WT1005-62 resolution test target. (a) Full FOV image. The pupil function and PSF of each small region denoted by (b1–e1) varied spatially, as shown in (b3–e3). The deconvolution results (b2–e2) show that the spatially varying aberrations were adequately corrected after processing. The inset frame enlarges part of the sample to indicate the enhanced resolution. (f) Line profiles through the line pairs in (b1–e1) (b2–e2) to highlight the aberration correction performance.

Figure 9

Results for the factory image. (a) Full FOV image captured by our inexpensive industrial lens. The pupil function and PSF of each small region denoted by (b1–d1) varied spatially, as shown in (b4–d4). The deconvolution results (b2–d2) show that the spatially varying aberrations were adequately corrected after processing. (b3–d3) The restored results using blind-estimated PSFs. (b5–d5) Line profiles at the underlined places in (b1–d1) (b2–d2) to show the improved image sharpness before and after correction using the proposed method. (e) The three images on the left are enlargements of the inset frames in (b1–d1), which are captured as blurred images in different FOV. The three images in the middle are enlargements of the inset frames in (b2–d2) and are the restored results corrected using the proposed method. The three images on the right are enlargements of the inset frames in (b3–d3), the results of the correction using the blind-estimation method.

Figure 10

Results for the building image. (a) Full FOV image captured by our inexpensive industrial lens. The pupil function and PSF of each small region denoted by (b1–d1) varied spatially, as shown in (b4–d4). The deconvolution results (b2–d2) show that the spatially varying aberrations were adequately corrected after processing. (b3–d3) The restored results using blind-estimated PSFs. (b5–d5) Line profiles at the underlined places in (b1–d1) (b2–d2) to show the improved image sharpness before and after correction using the proposed method. (e) The three images on the left are enlargements of the inset frames in (b1–d1), which are captured as blurred images in different FOV. The three images in the middle are enlargements of the inset frames in (b2–d2) and are the restored results corrected using the proposed method. The three images on the right are enlargements of the inset frames in (b3–d3), the results of the correction using the blind-estimation method..