we present a method to reduce the inherent errors caused by band-pass filter in off-axis quantitative phase microscopy and propose the optimum condition that can minimize these errors. We found that phase information of a sample in frequency domain nonlinearly oscillates as a function of the phase-shift correspond to the sample and its medium and the phase information of a sample inside the band-pass filter can be maximized by a proper phase-shift. Through numerical simulations and actual experiments, we demonstrate that the error in phase volume measurement can be effectively reduced by the enhancement of phase signal inside band-pass region using an optimum amount of phase that can be controlled by either changing medium index or wavelength of illumination.
INTRODUCTIONThe morphology or volume of phase objects such as biological cells [1] optical fibers [2,3], and micro particles [4] can be adequately measured by quantitative phase microscopy (QPM). This measurement can potentially be used for various biomedical and industrial applications. In the last decade, several types of QPM methods have been proposed: Fourier phase microscopy [5], Hilbert phase microscopy [6], diffraction phase microscopy [7], digital holographic microscopy [8], and complex-valued specimens based on noninterferometric imaging [9]. These methods have several advantages such as fast acquisition rate, high temporal stability and high spatial phase sensitivity. However, the accuracies of these QPM methods are limited by several inherent source of error such as impulse response of system that equivalent to a low pass filter (coherent transfer function) in spatial frequency of the field [10], numerical error used in phase extraction algorithm [11], noise sources usually caused by speckle [12] or the electronic noise and digitization error of a CCD [13]. There have been several attempts to reduce these unwanted errors. Auto-focusing and edge detection schemes [14] and focal-plane detection [15] were proposed to reduce the errors due to out-of-focus effects in the volume measurement. Most recently, new QPM systems using incoherent light sources have been proposed to decrease speckle effects in phase measurement [12].In this paper, we analyze the inherent error of QPM that mainly caused by coherent transfer function (CTF) of system or band-pass filter in frequency domain used in numerical phase calculation processes. We propose an optimum amount of phase existed that can effectively decrease the influence of band-pass filter. We show that phase signal in frequency domain nonlinearly depends on the phase-shift between sample and its medium and this nonlinearity can be applied for overcoming the unwanted effect of band-pass filter in frequency domain. Because we have freedom to adjust the phase-shift value by different methods such as changing illumination wavelength using tunable laser [16] or white-light source [17] or in some instances by alteration of refractive index of medium [18], or even the angle in dual illumination methods [19,20], our p...