Gram-Schmidt orthonormalization for retrieval of amplitude images under sinusoidal patterns of illumination

Authors: LU, YUZHEN - Michigan State University; LI, RICHARD - Michigan State University; Lu, Renfu

Submitted to: Applied Optics
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 8/2/2016
Publication Date: 8/23/2016
Citation: Lu, Y., Li, R., Lu, R. 2016. Gram-Schmidt orthonormalization for retrieval of amplitude images under sinusoidal patterns of illumination. Applied Optics. 55(5):6866-6873.

Interpretive Summary: To reduce food loss and waste due to inferior quality and improper postharvest handling in the horticultural industry, it is important that appropriate inspection technologies be developed and adopted at the critical points of harvest and postharvest handling operations. Machine vision technology is now being widely used for automatic inspection of external quality characteristics (size, color, shape and/or surface defects or texture) of horticultural and food products. The technology is generally implemented using uniform, diffuse illumination for acquisition of grayscale or color images from products. However, this popular imaging modality is still ineffective in detecting subtle surface defects or subsurface defects, such as bruise and internal browning in apples. Recently, a new structured-illumination reflectance imaging technique was developed in the ARS lab at East Lansing, Michigan, for enhanced detection of quality and defects in apples. This new imaging modality improves image contrast and spatial resolution as well as depth-varying characterization of biological tissues, and it was demonstrated to be effective for detecting surface and subsurface features or defects like bruises in apples that could have not been achieved with conventional imaging technique. However, the technique requires the acquisition of at least three images with each being spatially shifted by a specific phase angle. This research proposed a new mathematical method, based on Gram-Schmidt orthonormalization, for fast demodulation of the acquired images, a critical step for separating direct and amplitude component images from each acquired image. It was tested and evaluated through simulation studies as well as detection of bruises for ‘Gala’ and ‘Jonagold’ apples. The new method only needs two images with arbitrary phase shifts, and it achieved good results that are comparable to that by conventional demodulation method with three images. The method is fast and easy to implement and, hence, can improve the image acquisition speed for structured-illumination imaging.

Technical Abstract: Structured illumination using sinusoidal patterns has been utilized for optical imaging of biological tissues in biomedical research and, of horticultural products. Implementation of structured-illumination imaging relies on retrieval of amplitude images, which is conventionally achieved by a phase-shifting technique that requires collecting a minimum of three phase-shifted images. In this study, we proposed Gram-Schmidt orthonormalization (GSO) to retrieve amplitude component images using only two phase-shifted images. Two forms of GSO implementation were proposed, and prior to GSO processing, the direct component background was eliminated by subtracting a direct component image that was recovered using a spiral phase function in the Fourier space. We demonstrated the GSO methods through numerical simulations and application examples of detection of bruise defects in apples by structured-illumination reflectance imaging. GSO was comparable in performance to conventional three-phase based demodulation. It is simple, fast and effective for amplitude retrieval, and requires no prior phase information, which could facilitate fast implementation of structured-illumination imaging.