Employment of Fizeau fringe disintegration to magnify small phase variations

Abstract

When an object produces a small phase variation not less than the minimum phase variation detectable by the used system and more than the system’s noise, the object is considered as a tiny (or small) object. The measurement of interferometric phase differences evolved from a tiny optical phase object has gained attention in recent years due to its usefulness in accurate detection of nanometric dimensions. In the current work, a Fizeau wedge interferometer is used as an aberrationless method to amplify phase variations of a tiny object. The phase object is inserted between the two semi-reflecting/partially transmitting plates making a small wedge angle in between. The fast Fourier transformation (FFT) spectrum of the obtained interferograms is characterized by some frequency equidistant peaks. The number of these peaks is related to the number of the interfered rays and each peak represents a set of two-beam interferences. We applied a mask to select one of these peaks and reproduced its corresponding optical phase map via employing inverse fast Fourier transformation. The produced map contains the magnified phase variation with a magnification factor equal to 2 times the selected peak’s order. Experimental verification of two different phase object samples to amplify their phase variations with different amplification factors is performed. An integrated magnified phase by the object is calculated to test the validity of the proposed method. It is found that the magnification according to the selection of different FFT peaks is a little bit deviated from the expected magnification factors which is referred to ignoring refraction of the optical rays by the object. In spite of these deviations, good results are obtained.

Spatio-temporal photolysis rate profiles of UV254 irradiated toluene

“…Accordingly, if a number 10 Δm is counted from the beginning of both experiments, it is found that this number takes place in a shorter time ( t = 502 s) when the irradiation is from above compared with the longer time ( t = 838 s) in the other case of irradiation. Based on the FFT analyses of these interferograms 37 , 47 , 48 , the reconstructed wrapped phase maps are shown in Fig. 3 while Fig.…”

“…frequency) of a certain behavior of fringes’ distribution. Afterwards, applying the inverse fast Fourier transformation (IFFT) according to the procedure described elsewhere 37 , 47 , 48 to obtain the 2D phase map can be implemented.…”