Phase Retrieval by Flattening the Wavefront

Abstract

Many objects of interest in imaging, such as biological cells or turbulent air, are phase-only objects that are transparent and thus produce little to no contrast in wide-field microscopes. The phase accumulated by this light carries important information about the refractive index and the thickness of the object. We propose a method for retrieving the phase by using a spatial light modulator (slm) to conjugate the phase of the object, flattening the wavefront of light passing through the slm and the object. After we flatten the wavefront, the resulting configuration on the slm is the conjugate of the phase image, which we can easily invert to recover the original phase image. This method retrieves the phase without using any prior knowledge about the object. Our algorithm performs a decomposition of the image into basis functions and searches for the coefficients that yield the flattest output intensity pattern. This algorithm takes advantage of the fact that a relatively small number of basis elements can store the majority of the information in the image. Popular phase retrieval methods such as the Gerchberg–Saxton algorithm can only converge to the phase image under light that is sufficiently coherent. From our simulations, we find that our method consistently produces correlations of over 99% with the original phase image, using either incoherent or coherent light and only 10% as many basis elements as the number of pixels in the image. We believe this result is a strong indication that this method will be able to reliably retrieve a direct phase image in the laboratory.