To simulate the effects of multiple-longitudinal modes and rapid fluctuations in center frequency, we use sinusoidal phase modulation and linewidth broadening, respectively. These effects allow us to degrade the temporal coherence of our master-oscillator laser, which we then use to conduct digital holography experiments. In turn, our results show that the coherence efficiency decreases quadratically with fringe visibility and that our measurements agree with our models to within 1.8% for sinusoidal phase modulation and 6.9% for linewidth broadening.
Digital holography (DH) has been demonstrated to be an effective wave-front sensor in low signal-to-noise ratio (SNR) environments due to the use of a strong reference. However, since DH relies on the interference of a signal with the mutually coherent reference, the coherence properties of the master-oscillator (MO) laser can degrade system SNR at long ranges. In this paper, a DH system in the off-axis image plane recording geometry was assembled and used to measure the effects of the MO coherence properties on the SNR. The coherence properties of the MO laser were degraded using sinusoidal phase modulation, which imparted maximum phase shifts of 0.38π, 0.55π, and 0.73π, at modulation frequencies of 20MHz to 100MHz. The measured coherence efficiency losses were closely predicted by the square of the fringe visibility, and deviated from the theoretical predictions by root-mean-squared errors of 0.0397, 0.0373, and 0.1007 for the three depths of modulation, respectively. The empirical data and models presented in this work may be used to assess efficiency losses in a DH system due to coherence effects.
This paper measures the mixing efficiency of a digital holography system at various optical path differences and hologram integrations times. From the measurements, the master oscillator (MO) laser spectral lineshape and linewidth is estimated. The lineshape was Gaussian, which is indicative of laser frequency flicker noise or 1/f noise, and the linewidth decreased by 65% when the integration time was decreased from 100 ms to 0.1 ms. This reduction in the observed MO laser linewidth yields an increased coherence length and time of 280%. A flicker noise model for the linewidth and integration time is used and approximates the measurements to within 17%.
The US Air Force (USAF) conducts research involving the sensing and compensation of atmospheric turbulence, which acts to blur images and make laser-beam propagation more challenging. As such, USAF scientists and engineers (S and Es) often face the challenging task of explaining this research to audiences without relevant technical expertise. These audiences vary widely all the way from upper military leadership down to K-12 students as part of science, technology, engineering, and mathematics (STEM) outreach activities. Previously, a team of USAF S and Es developed a table-top setup for the demonstration of digital-holography (DH) technology. This technology enables the measurement of the complex-optical field, which in turn enables a plethora of applications that involve imaging and wavefront sensing. Therefore, in this paper we extend this table-top setup to illustrate both the effects of atmospheric turbulence on the imaging and wavefront sensing process and the digital-signal processing required to estimate and mitigate these effects. The enhanced demonstration provides a visual-learning aid to help explain the complicated concepts associated with imaging through atmospheric turbulence. Specifically, we show that we can introduce aberrations into the DH system and use digital-image correction to refocus the resultant blurry images. This paper discusses the overall system design, improvements, and lessons learned.
The SPIE Student Chapter at the Air Force Institute of Technology (AFIT) is spearheading a new outreach project to encourage science, technology, engineering, and mathematics (STEM) in grades K-12. This new outreach project is referred to as the Digital Holography Demonstration (DHD). Using a table-top setup, the DHD estimates the both the amplitude and phase of the complex-optical field, and in so doing, illustrates several fundamental optics and photonics principles including diffraction, refraction, and the interference of light. These fundamental optics and photonics principles have direct ties to current technologies being developed in the medical, astronomy, and defense communities (to name a few). This paper celebrates the resourcefulness of the DHD for STEM-based outreach events and provides a parts list, cost breakdown, and brochures, so that future efforts can benefit from its design.
This paper uses wave-optics simulations to explore the validity of signal-to-noise models for digital-holographic detection. In practice, digital-holographic detection provides access to an estimate of the complex-optical field which is of utility to long-range imaging applications. The analysis starts with an overview of the various recording geometries used within the open literature (i.e., the on-axis phase shifting recording geometry, the off-axis pupil plane recording geometry, and the off-axis image plane recording geometry). It then provides an overview of the closed-form expressions for the signal-to-noise ratios used for the various recording geometries of interest. This overview contains an explanation of the assumptions used within to write the closed-form expressions in terms of the mean number of photoelectrons associated with both the signal and reference beams. Next, the analysis formulates an illustrative example with weak, moderately deep, and deep turbulence conditions. This illustrative example provides the grounds in which to rewrite the closed-form expressions in terms of the illuminator power. It also enables a validation study using wave-optics simulations. The results show that the signal-to-noise models are, in general, accurate with respect to the percentage error associated with a performance metric referred to as the field-estimated Strehl ratio.
This paper compares efficiency measurements to predictions for a digital-holography system operating in the off-axis image plane recording geometry. We use a highly coherent 532 nm laser source, an extended Spectralon object, and an Si focal-plane array to perform digital-holographic detection, which provides access to an estimate of the complex-optical field and is of utility to long-range imaging applications. In the experiments, digitalholographic detection results from the interference of a signal beam with a reference beam. The signal beam was created from the active illumination of the extended Spectralon object and the reference beam from a local oscillator which is split off from the master-oscillator 532 nm laser source. To compare efficiency measurements to predictions, an expression was developed for the signal-to-noise ratio, which contains many multiplicative terms with respect to total-system efficiency. In the best case, the measured total efficiency was 15.2% ± 5.8% as compared to the predicted 16.4%. The results show that the polarization and the fringe-integration efficiency terms play the largest role in the total-system efficiency.
The effects of deep turbulence in long-range imaging applications presents unique challenges to properly measure and correct for aberrations incurred along the atmospheric path. In practice, digital holography can detect the path-integrated wavefront distortions caused by deep turbulence, and di
erent recording geometries offer different benefits depending on the application of interest. Previous studies have evaluated the performance of the off-axis image and pupil plane recording geometries for deep-turbulence sensing. This study models digital holography in the on-axis phase shifting recording geometry using wave optics simulations. In particular, the analysis models spherical-wave propagation through varying deep-turbulence conditions to estimate the complex optical field, and performance is evaluated by calculating the field-estimated Strehl ratio and RMS wavefront error. Altogether, the results show that digital holography in the on-axis phase shifting recording geometry is an effective wavefront-sensing method in the presence of deep turbulence.