Refining common path interferometry with a spiral phase Fourier filter

Recently, spiral phase filtering for isotropic edge enhancement and for optical thickness measurements of phase samples has been implemented in microscopy, using gray value images on a spatial light modulator (SLM) placed in a Fourier plane of the sample. In a common path interferometer, the light going through the central part of the helical phase hologram is overlapped with the light passing through the periphery of the phase filter. Replacing the center by a disk of uniform phase leads to pseudo-relief images, with the apparent illumination direction depending on the gray level of the central area. If one uses such images to reconstruct the optical thickness of phase objects, the reference wave through the central part ideally should have a plane wavefront. This is normally not the case, especially when the imaging setup requires a relatively large central area around the DC Fourier component. This paper shows how a direct measurement of the amplitude of the reference beam, which can be done in the given setup by simply changing the image on the SLM, can increase the accuracy of phase measurement, allowing one to determine the refractive index with a relative error below 0.6%.