Performance analysis of phase retrieval using transport of intensity with digital holography [Invited]

Abstract

The performance of direct and unwrapped phase retrieval, which combines digital holography with the transport of intensity, is examined in detail in this paper. In this technique, digital holography is used to numerically reconstruct the intensities at different planes around the image plane, and phase retrieval is achieved by the transport of intensity. Digital holography with transport of intensity is examined for inline and off-axis geometries. The effect of twin images in the inline case is evaluated. Phase-shifting digital holography with transport of intensity is introduced. The performance of digital holography with transport of intensity is compared with traditional off-axis single- and dual-wavelength techniques, which employ standard phase unwrapping algorithms. Simulations and experiments are performed to determine and compare the accuracy of phase retrieval through a mean-squared-error figure of merit as well as the computational speeds of the various methods.

Non-recursive transport of intensity phase retrieval with the transport of phase

“…The defocused intensity images in the simulations are generated by using the nonparaxial diffraction formula. Since the optical fields need to be propagated in a very small distance (micro-scale) [18], the distances from the defocused planes to the focal (image) plane are set as ± z. The (nonparaxial) impulse response for optical propagation can be expressed as [19]…”

Computational Method for Wavefront Sensing Based on Transport-of-Intensity Equation

“…In our simulation, there is no noise, so the step value is limited only from above, which is observed in the obtained dependence (Figure 6). More thorough study on the accuracy in the displacement of the between planes where intensity distributions were acquired was carried out in [49]. During the second numerical simulation, the influence of the step value ∂z was investigated for the following parameters: R0 = 100 mm; z = 80, 80 + ∂z, 80 + 2∂z, …, R0; ∂z = 0.1, 1, 5, 10 mm.…”

“…In our simulation, there is no noise, so the step value is limited only from above, which is observed in the obtained dependence (Figure 6). More thorough study on the accuracy in the displacement of the between planes where intensity distributions were acquired was carried out in [49]. Note that it is difficult to find the exact value of the chord l near R0 due to the effect of sampling.…”

Digital holography for real-time detection based on femtosecond laser

“…3,4 Digital holography provides a way to measure optical phase data and typically delivers 3-D surface or optical thickness images. Several recording and processing schemes have been developed to assess optical wave characteristics, such as amplitude, phase, and polarization, which make digital holography a very powerful method for 3-D imaging and displaying, [5][6][7] phase retrieval, [8][9][10] and wavefront sensing. [11][12][13] Femtosecond pulsed laser is the shortest pulse that can be obtained under today's technique.…”