An experimental setup for optical phase extraction from 2-D interferograms using a one-shot phase-shifting technique able to achieve four interferograms with 90° phase shifts in between is presented. The system uses a common-path interferometer consisting of two windows in the input plane and a phase grating in Fourier plane as its pupil. Each window has a birefringent wave plate attached in order to achieve nearly circular polarization of opposite rotations one respect to the other after being illuminated with a 45° linear polarized beam. In the output, interference of the fields associated with replicated windows (diffraction orders) is achieved by a proper choice of the windows spacing with respect to the grating period. The phase shifts to achieve four interferograms simultaneously to perform phase-shifting interferometry can be obtained by placing linear polarizers on each diffraction orders before detection at an appropriate angle. Some experimental results are shown.

One-shot phase-shifting phase-grating interferometry with modulation of polarization: case of four interferograms.

A modified holographic interferometer is described which enables automatic fringe pattern analysis to be achieved when recording transient events. The introduction of a phase grating enables the method of phase-stepping fringe analysis to be applied to a wide range of measurement problems. The theory is developed, and an analysis of the sources of error is presented with the aid of computer simulations. Initial experimental results confirm the utility of the method and its potential application in pulsed laser holography. The method can in principle be applied to electronic speckle pattern interferometry.

Multichannel phase-stepped holographic interferometry

We describe two new techniques for spatial phase stepping using a computer-generated holographic optical element (HOE). The techniques are implemented with electronic speckle pattern interferom- etry, although they could be applied to other optical metrology methods. The first technique uses an HOE that introduces a known phase step between the 61 diffracted orders, without being translated. The interfer- ence phase corresponding to object deformation can be calculated from a single TV frame, and the technique is therefore suitable for the mea- surement of transient deformations. We apply the technique to measure the phase changes caused by refractive index variations in an evolving thermal plume. The second technique requires the HOE to be used in conjunction with a phase grating. In this technique, the HOE and the phase grating are used sequentially for the two exposures required in speckle interferometry (made before and after object deformation) and is therefore suitable for making dynamic deformation measurements with a double-pulsed interferometer. A root mean square (rms) precision of 2p/20 rad for the phase measurements is obtained. © 1999 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(99)00712-6)

Spatial phase-stepped interferometry using a holographic optical element

An optical configuration for parallel two-step phase-shifting digital holographic microscopy (DHM) based on a grating pair is proposed for the purpose of real-time phase microscopy. Orthogonally circularly polarized object and reference waves are diffracted twice by a pair of gratings, and two parallel copies for each beams come into being. Combined with polarization elements, parallel two-step phase-shifting holograms are obtained. Based on the proposed configuration, two schemes of DHM, i.e., slightly off-axis and on-axis DHM, have been implemented. The slightly off-axis DHM suppresses the dc term by subtracting the two phase-shifting holograms from each other, thus the requirement on the off-axis angle and sampling power of the CCD camera is reduced greatly. The on-axis DHM has the least requirement on the resolving power of the CCD camera, while it requires that the reference wave is premeasured and its intensity is no less than 2 times the maximal intensity of the object wave.

Parallel two-step phase-shifting digital holograph microscopy based on a grating pair

We present a technique to measure the mechanical complex amplitude, i.e. the mechanical amplitude and phase of vibration, of an ultrasonic plane wavefield of nanometric amplitude that propagates on a surface. Our aim is to detect perturbations of the initially smooth wavefronts that indicate the presence of flaws in the material. We use bursts of surface acoustic waves (SAWs) and a double-pulsed TV holography system that records two correlograms with time separations down to 1.5 µs. The phases of the correlograms are calculated separately using the spatial Fourier transform method (SFTM) and operated on to obtain the phase change between exposures. In the resultant optical phase map, the field of instantaneous displacements of the surface (that comprises several periods of the SAW) acts as a modulated spatial carrier, now related to the mechanical phase and amplitude, that are extracted by applying the SFTM again.

https://iopscience.iop.org/article/10.1088/0957-0233/14/12/012/pdf

Measurement of the complex amplitude of transient surface acoustic waves using double-pulsed TV holography and a two-stage spatial Fourier transform method

We have used a computer-generated holographic optical element
(HOE) with electronic speckle pattern interferometry to calculate
the interference phase corresponding to the deformation of a test
object from a single TV frame. The HOE is a modified crossed phase
grating that introduces a known phase change between the ±1 diffracted
orders, without being translated. The progressive propagation of
transient mechanical waves was measured with an rms precision of
2π/30.

Theo Tschudi

Papers

Transient deformation measurement with electronic speckle pattern interferometry by use of a holographic optical element for spatial phase stepping