Axial multi-image phase retrieval under tilt illumination

Abstract

As a coherent diffractive imaging technique, axial multi-image phase retrieval utilizes a series of diffraction patterns on the basis of axial movement diversity to reconstruct full object wave field. Theoretically, fast convergence and high-accuracy of axial multi-image phase retrieval are demonstrated. In experiment, its retrieval suffers from the tilt illumination, in which diffraction patterns will shift in the lateral direction as the receiver traverses along the axis. In this case, the reconstructed result will be blurry or even mistaken. To solve this problem, we introduce cross-correlation calibration to derive the oblique angle and employ tilt diffraction into axial phase retrieval to recover a target, which is successfully demonstrated in simulation and experiment. Also, our method could provide a useful guidance for measuring how obliquely the incident light illuminates in an optical system.

Figure 1

The model of tilt diffraction: (a) The schematic of free-space diffractive imaging model with tilt illumination. (b) and (c) denote oblique modality in the case of tilt illumination or CCD.

Figure 2

The image reconstruction test using APR: (a) The diffraction boundary of tilt illumination. (b) The ground truth for test. (c) The LMSE distribution between ground truth and reconstructed amplitude by APR algorithm under tilt illumination.

Figure 3

The calibration of tilt illumination for APR algorithm: (a) The schematic of cross-correlation calibration. (b) The movement of the peak position of cross-correlation. (c) The LMSE curve in assigned circumstances. (d) and (e) denote the uncalibrated and calibrated reconstructed amplitude. (f) The diffraction disc of incident light in Z_n = 20 mm, 22 mm and 24 mm.

Figure 4

Experiment setup. A green fiber laser at the wavelength of 532 nm passes through pinhole and collimating lens to generate a plane wave. The plane wave shaped by aperture is used to illuminate the resolution chart to form a series of diffraction patterns with the initial distance Z₀ and interval d.

Figure 5

Recorded data and reconstructed complex amplitude in Z₀ = 50 mm, d = 2 mm, N = 16, M = 1000: (a) Diffraction disc of incident light in Z₁ = 50 mm. (b) Diffraction pattern in Z₁ = 50 mm. (c) The movement of the peak position of cross-correlation; (d) and (e) are reconstructed amplitude and phase by APR algorithm, respectively; (f) and (g) are reconstructed amplitude and phase by APRT algorithm, respectively. Here iterative number is equal to 1000.

Figure 6

Recorded data and reconstructed complex amplitude in Z₀ = 60 mm, d = 1 mm, N = 13, M = 800: (a) Diffraction disc of incident light in Z₁ = 60 mm. (b) Diffraction pattern in Z₁ = 60 mm. (c) The movement of the peak position of cross-correlation; (d) and (e) are reconstructed amplitude and phase by APR algorithm, respectively; (f) and (g) are reconstructed amplitude and phase by APRT algorithm, respectively. Here iterative number is fixed at 2000.

Figure 7

The reconstructed phase with different angle compensation: (a) Retrieved amplitude distribution. (b) MAG curve, (c) Retrieved phase patterns.