Pixelated mask spatial carrier phase shifting interferometry algorithms and associated errors

Abstract

In both temporal and spatial carrier phase shifting interferometry, the primary source of phase calculation error results from an error in the relative phase shift between sample points. In spatial carrier phase shifting interferometry, this phase shifting error is caused directly by the wavefront under test and is unavoidable. In order to minimize the phase shifting error, a pixelated spatial carrier phase shifting technique has been developed by 4D technologies. This new technique allows for the grouping of phase shifted pixels together around a single point in two dimensions, minimizing the phase shift change due to the spatial variation in the test wavefront. A formula for the phase calculation error in spatial carrier phase shifting interferometry is derived. The error associated with the use of linear N-point averaging algorithms is presented and compared with those of the pixelated spatial carrier technique.

Utilizing Quantitative Phase Microscopy to Observe Cellular Response to Treatment and Dynamic Behaviors

“…It operates at a wavelength of 511nm or 660nm and utilizes a Linnik interference objective at a magnification of 20X NA 0.45 and 50X NA 0.8 with additional magnification obtained via a flip-in 2X field of view (FOV) lens. The camera is an Illunis XMV-2020 with a Moxtek pixelated phase mask to enable spatial phase measurement with short exposures (<1ms) at frame rates as high as 15fps to freeze motion while being insensitive to vibration [3,4]. For the examples in this paper, objects are viewed in double pass on a reflective surface as shown in Figure 1.…”

Spatial-carrier phase-shifting digital holography utilizing spatial frequency analysis for the correction of the phase-shift error

“…Then, several single-shot inline phase-shifting techniques [8-10] were proposed to achieve instantaneous measurement without the unwanted images. However, in these techniques, either an array of optical devices [8], a grating [9], or the measurement of the complex amplitude of the reference wave [10] is required, and the optical implementations of each technique are complicated.Recently, SCPS interferometry [11,12] has been applied to digital holography to achieve instantaneous measurement using a simple setup [13][14][15][16]. In this technique, however, it has been reported that the phase-shift error is inherently occurred by the phase shift of the object wave against that of the reference wave [12].…”

“…Recently, SCPS interferometry [11,12] has been applied to digital holography to achieve instantaneous measurement using a simple setup [13][14][15][16]. In this technique, however, it has been reported that the phase-shift error is inherently occurred by the phase shift of the object wave against that of the reference wave [12].…”

“…In this technique, however, it has been reported that the phase-shift error is inherently occurred by the phase shift of the object wave against that of the reference wave [12]. This means that the phase-shift error always occurs unless the angle between the optical axis and the reference wave is quite accurately adjusted and the object wave is plane wave.…”

“…θ was set to be sin −1 λ∕3τ against the optical axis of a model. Although we assume that the amplitude of the object wave hardly varies at the neighboring pixels, which is the same situation with other spatial phase-shifting techniques [8][9][10][11][12][13][14][15][16], it is not always true, especially when measuring rough-surfaced objects. This time, the minimum correction value of amplitude, sinτ∕2f2π∕λ sin θ − k x g in Eq.…”