Wave-front control of a large-aperture laser system by use of a static phase corrector

Polarizing white light interferometry for phase measurements using two simultaneous interferograms

Our research introduces a design for a polarization phase-shifting white light interferometric system (PPS-WLIS) that operates in a transmissive mode for measuring the slope phase of transparent objects. It comprises a cyclic path interferometer (lateral shear interferometer) coupled with a multiplexing Michelson interferometer. The system uses polarization to produce two parallel interferograms with polarization modulated with relative shifts simultaneously. To determine the optical phase, we used a two-step algorithm for phase demodulation that does not necessitate precise phase shifts, making the system more straightforward to operate. As a result, we could observe variations in the object associated with optical phase changes. Furthermore, our method simplifies the phase-shift interferometry process by requiring only one capture, making it an effective way to examine objects at dynamic events. As an illustration, we demonstrated the temperature measurement generated by a section of a candle flame.

All-fiber orthogonal-polarized white-noise-modulated laser for short-coherence dynamic interferometry

An all-fiber orthogonal-polarized white-noise-modulated laser (AOWL) for short-coherence dynamic interferometry is proposed. Short-coherence laser is achieved by current modulating of a laser diode with the band-limited white noise. A pair of orthogonal-polarized lights with adjustable delay for short-coherence dynamic interferometry are output by the all-fiber structure. In the non-common-path interferometry, the AOWL can significantly suppress the interference signal clutter with 73% side lobe suppression ratio, that improves the positioning accuracy of zero optical path difference. The wavefront aberrations of a parallel plate are measured with the AOWL in the common-path dynamic interferometers, avoiding the fringe crosstalk.

Radial polarizing phase-shifting interferometry with applications to single-shot n interferogram measurements and potential usage for white light interferogram analysis

In this research, we present an interferometric system to analyze transparent samples using interferograms generated by a phase-shifting radial shear grating interferometer for two cases: the first obtaining n simultaneous phase-shifting interferograms using a coherent light source and the second one using sequential phase steps with a white light source. For the first case, the simultaneous interferograms are generated using two optical systems: the first one generates the polarized pattern while the second one consists of a 4f system creating replicas of the output interferograms. By using a 2D sinusoidal phase grating, we have the advantage of obtaining up to nine replicated interferograms, all of them with comparable intensities and having amplitudes modulated by the 2D sinusoidal phase grating diffraction orders as zero-order Bessel's functions. To obtain the optical phase map, several phase shifts are generated by placing a polarizing filter covering each replicated interferogram. We highlight the advantage of using n simultaneous interferograms by comparing resulting optical phases processed by a conventional four-step algorithm against those obtained by an implemented n=N+1 method, reducing errors with noisy interferograms. Results for n=7 and n=9 cases are presented. In addition, we have tested the setup with white light interference techniques by employing the polarizer radial shearing interferometer; for this case, the optical phase is calculated with the four-step and the three-step algorithms. Results of testing the developed system to examine static and dynamic phase objects are also included.

Parallel phase shifting radial shear interferometry with complex fringes and unknown phase shift

We present an interferometric method to analyze transparent samples using complex fringes generated by a parallel phase shifting radial shear interferometer using two coupled interferometers. Parallel interferograms are generated using two interferometers: the first one generates the polarized base pattern, and the second system is used to generate parallel interferograms allowing the adjustment of the x-y positions of the parallel interferograms. To obtain the optical phase map, parallel phase shift is generated by collocating polarizing filters at the output of the system; the polarizers are placed at arbitrary angles since they do not require adjustment because of the phase-recovery algorithm. The optical phase was processed using a two-step algorithm based on a modified Gram-Schmidt orthogonalization method. Such an algorithm has the advantage of not being iterative and is robust to amplitude modulation. The proposed method reduces the number of captures needed in phase-shifting interferometry. We applied the developed system to examine static and dynamics phase objects.

Time-resolved thermally induced aberrations in a flash-lamp pumped Nd:Glass disk amplifier using a 2 × 2 position sensitive detector array

A novel technique of measuring the prompt, thermally induced wave-front aberrations in a large aperture flash-lamp pumped Nd³⁺ glass disk amplifier is presented. Implementing a 2 × 2 lens array and a 2 × 2 position sensitive detector array as a diagnostic system, the wave-front profile was successfully reconstructed for the first five Zernike terms for a temporal window of 8.5 ms.

Automatic low-order aberration correction based on geometrical optics for slab lasers

In this paper, we present a method based on geometry optics to simultaneously correct low-order aberrations and reshape the beams of slab lasers. A coaxial optical system with three lenses is adapted. The positions of the three lenses are directly calculated based on the beam parameters detected by wavefront sensors. The initial sizes of the input beams are 1.8  mm×11  mm, and peak-to-valley (PV) values of the wavefront range up to several tens of microns. After automatic correction, the dimensions may reach nearly 22  mm×22  mm as expected, and PV values of the wavefront are less than 2 μm. The effectiveness and precision of this method are verified with experiments.

Lensless reflective point diffraction interferometer

A lensless reflective point diffraction interferometer (LRPDI) is proposed for dynamic wavefront measurement. The point diffraction interferometer is integrated on a small substrate with properly designed thin film, which is used for generating the interferogram with high carrier frequency at a CCD target. By lensless imaging, the complex amplitude at the CCD target can be propagated to the conjugated plane of the exit pupil of an incident wavefront, which not only avoids the edge diffraction in the interferogram, but also eliminates systematic error. The accuracy of LRPDI is demonstrated by simulation and experiment, and a precision better than 1/150 wavelength is achieved. The new design with lensless imaging processing is suitable for dynamic wavefront measurement.

Single-shot reflective shearing point diffraction interferometer for wavefront measurements

A single-shot reflective shearing point diffraction interferometer (S-SRSPDI) is designed for large-aperture dynamic wavefront measurements. The PDI is integrated on the small substrate with properly designed thin film. The wavefront under test is reflected by the front and rear surfaces of the substrate respectively to generate an interferogram with high linear-carrier frequency, which is used to reconstruct the wavefront by means of the Fourier transform algorithm. In this paper, the analytic formula of intensity distribution of the interferogram is derived. The parameters related with the carrier frequency of fringes are discussed. The method to optimize the contrast of the interferogram is proposed by analyzing the reflective polarization effects. In addition, the spurious fringes of the interferogram are removed by the proper designed blocking film. S-SRSPDI was applied to detect the dynamic wavefront with a diameter of 400 mm. The measured aberrations are in good agreement with those obtained by the shearing method, which verifies that the proposed S-SRSPDI is a powerful tool for large-aperture dynamic wavefront measurements.

A single-shot common-path phase-stepping radial shearing interferometer for wavefront measurements

A single-shot common-path phase-stepping radial shearing interferometer (RSI) is proposed for wavefront measurements. In the proposed RSI, three quarter-wave plates are used as phase shifters to produce four spatially separated phase-stepping fringe patterns that are recorded simultaneously by a single CCD camera. The proposed RSI can measure the wavefront under test in real-time, and it is also insensitive to environmental vibration due to its common-path structure. Experimentally the proposed RSI is applied to detect the distorted wavefronts generated by a liquid crystal spatial light modulator. The measured aberrations are in good agreement with that obtained with (by) a Hartmann-Shack wavefront sensor, indicating that the proposed RSI is a useful tool for wavefront measurements.