Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Summary

A method for overcoming the optical diffraction limit is presented. The method includes a two-step process: optical phase retrieval using iterative Gerchberg-Saxton algorithm, and imaging system shifting followed by repetition of the first step. A synthetically increased lens aperture is generated along the direction of movement, yielding higher imaging resolution.

Abstract

We propose a method for increasing the resolution of an object and overcoming the diffraction limit of an optical system installed on top of a moving imaging system, such as an airborne platform or satellite. The resolution improvement is obtained in a two-step process. First, three low resolution differently defocused images are being captured and the optical phase is retrieved using an improved iterative Gerchberg-Saxton based algorithm. The phase retrieval allows to numerically back propagate the field to the aperture plane. Second, the imaging system is shifted and the first step is repeated. The obtained optical fields at the aperture plane are combined and a synthetically increased lens aperture is generated along the direction of movement, yielding higher imaging resolution. The method resembles a well-known approach from the microwave regime called the Synthetic Aperture Radar (SAR) in which the antenna size is synthetically increased along the platform propagation direction. The proposed method is demonstrated through laboratory experiment.

Introduction

In radar imaging, a narrow angle beam of pulse Radio Frequency (RF) is transmitted using an antenna that is mounted on a platform. The radar signal transmits in a side-looking direction towards the surface^1,2. The reflected signal is backscattered from the surface and is received by the same antenna². The received signals are converted to a radar image. In Real Aperture Radar (RAR) the resolution in the azimuth direction is proportional to wavelength and inversely proportional to the aperture dimension³. Thus, a bigger antenna is required for higher azimuth resolution. However, it is difficult to attach large antenna to a moving platfo....

Protocol

1. Setup Alignment

1. Start by roughly aligning the laser, the beam expender, the lens, and the camera on the same axis; this would be the optic axis.
2. Turn on the laser (without the USAT target), and make sure that the light passes through the center of the lens. Use an aperture iris to verify.
3. Turn on the camera, and make sure that the light focuses on the center of the camera.
4. Shift back the camera, using the linear z stage. Since the system is going out of focus, the spot of light will grow. Make sure that the center of the spot remains in the same lateral position. If not, carefully change the position of the imaging system a....

Results

An example for the nine captured images (three defocus images in three lateral positions) is shown in Figure 3.

An example for the G-S convergence is shown in Figure 4. The correlation coefficient for the central image I_1,b is above 0.95, and the correlation coefficient for the side images I_1,a, and I_1,c is above 0.85 (in full numerical simulation they all passed 0.99).

A representative result for th.......

Discussion

The optical synthetic aperture RADAR (OSAR) concept that is presented in this paper is a new super resolved approach that uses the G-S algorithm and scanning technique in order to improve the spatial resolution of an object in the direction of the scan. The movement of the imaging platform can be self-generated while using an airborne or satellite platform. Unlike many time multiplexing SR techniques, our method does not require any a priori information of the object, other than the fact that it is stationary du.......

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Red Laser Module	Thorlabs	LDM635
10X Galilean Beam Expander	Thorlabs	BE10M-A
Negative 1951 USAF Test Target	Thorlabs	R3L3S1N
Filter holder for 2 in Square Filters	Thorlabs	FH2
1 in Linear Translation Stage	Thorlabs	PT1	2x
Lens Mount for Ø1 in Optics	Thorlabs	LMR1
Lens f = 100.0 mm	Thorlabs	AC254-100-A
Graduated Ring-Activated Iris Diaphragm	Thorlabs	SM1D12C
2.5 mm x 2.5 mm Aperture Ø1 in			Indoor production
High Resolution CMOS Camera	Thorlabs	DCC1545M