Quadratic Phase Distortion Research Articles

Sampling moiré method: a tool for sensing quadratic phase distortion and its correction for accurate quantitative phase microscopy.

The advantages of quantitative phase microscopy (QPM) such as label-free imaging with high spatial sensitivity, live cell compatibility and high-speed imaging makes it viable for various biological applications. The measurement accuracy of QPM strongly relies on the shape of the recorded interferograms, whether straight or curved fringes are recorded during the data acquisition. Moreover, for a single shot phase recovery high fringe density is required. The wavefront curvature for the high-density fringes over the entire field of view is difficult to be discerned with the naked eye. As a consequence, there is a quadratic phase aberration in the recovered phase images due to curvature mismatch. In the present work, we have implemented sampling moiré method for real-time sensing of the wavefront curvature mismatch between the object and the reference wavefronts and further for its correction. By zooming out the interferogram, moiré fringes are generated which helps to easily identify the curvature of the fringes. The wavefront curvature mismatch correction accuracy of the method is tested with the help of low temporal coherent light source such as a white light (temporal coherence ∼ 1.6 µm). The proposed scheme is successfully demonstrated to remove the quadratic phase aberration caused due to wavefront mismatch from an USAF resolution target and the biological tissue samples. The phase recovery accuracy of the current scheme is further compared with and found to better than the standard method called principle component analysis. The proposed method enables recording of the corrected wavefront interferogram without needing any additional optical components or modification and also does not need any post-processing correction algorithms. The proposed method of curvature compensation paves the path for a high-throughput and accurate quantitative phase imaging.

Precise Measurement of Fiber Third-Order Dispersion Using Transfer Function of a Microwave Photonic Filter

Third-order dispersion (TOD) is a fundamental parameter to characterize optical fiber. In this paper, we propose a method to precisely measure TOD of an optical fiber by using the amplitude and phase transfer function of a microwave photonic filter (MPF). The fiber under test (FUT) plays an important role in the MPF, of which the transfer function has a quadratic phase distortion due to the TOD of the FUT. Through iteratively modifying the quadratic phase spectral coefficient of the optical signal in the MPF to counteract the TOD effect, the transfer function distortion can be almost compensated. According to the definite relationship between the TOD and the compensation coefficient, we can determine the TOD precisely. In the experiment, the measurement uncertainty of 0.2% is obtained of a dispersion compensating fiber, designed for the compensation of 80 km standard fiber.

Aberration compensation for objective phase curvature in phase holographic microscopy: comment

In a recent Letter by Seo et al. [Opt. Lett.37, 4976 (2012)], the numerical correction of the quadratic phase distortion introduced by the microscope objective in digital holographic microscopy (DHM) has been presented. In this comment, we would like to draw to the attention of the authors and the readers in general that this approach could not be the optimal solution for maintaining the accuracy of the quantitative phase via DHM. We recall that the use of telecentric imaging systems in DHM simplifies the numerical processing of the phase images and produces more accurate measurements.

Characterization and compensation of phase distortions in holograms for generating and detecting doughnut beams

Raster scan systems can introduce cubic and quadratic phase distortions in holograms for generating and detecting doughnut beams. The distortions can be corrected by subtracting corresponding terms from the hologram design. The compensation parameters can be determined by fabricating test holograms and applying rotational symmetry analysis to the intensity distribution of the generated beams. The 2- and 3-fold rotational symmetry components are shown to be effective in determining quadratic and cubic corrections respectively, and in the final corrected hologram the total contribution of anisotropic intensity components was reduced to 0.3%.

An Analysis of ISAR Image Distortion Based on the Phase Modulation Effect

Distortion in the ISAR image of a target is a result of nonuniform rotational motion of the target during the imaging period. In many of the measured ISAR images from moving targets, such as those from in-flight aircraft, the distortion can be quite severe. Often, the image integration time is only a few seconds in duration and the target's rotational displacement is only a few degrees. The conventional quadratic phase distortion effect is not adequate in explaining the severe blurring in many of these observations. A numerical model based on a time-varying target rotation rate has been developed to quantify the distortion in the ISAR image. It has successfully modelled the severe distortion observed; the model's simulated results are validated by experimental data. Results from the analysis indicate that the severe distortion is attributed to the phase modulation effect where a time-varying Doppler frequency provides the smearing mechanism. For target identification applications, an efficient method on refocusing distorted ISAR images based on time-frequency analysis has also been developed based on the insights obtained from the results of the numerical modelling and experimental investigation conducted in this study.

Effects of quadratic phase distortion on correlator performance

The deformable mirror spatial light modulator (SLM) has an inherent distortion characteristic that can be approximated as a square-law transfer function. We examine the result of this distortion when this SLM is used in an optical correlator.

Optical Correlation of Fresnel Images

A real-time optical correlator is described that uses an ultrasonic light modulator (ULM) in conjunction with an amplitude mask or replica of the signal to achieve linear, phase-coherent detection, without need for high quality optics. When the mask is placed in a Fresnel image plane of the ULM, optimum correlation and collinear heterodyning are achieved. Correlator response has been calculated and measured as a function of mask-ULM separation for a pulse modulated cw signal and a square wave modulated fm waveform. For essentially band-limited signals, the output is a pair of symmetrically time-shifted, matched filter responses, possessing negligible quadratic phase distortion.

Intermodulation Distortion in Analog FM Troposcatter Systems

In broadband transmission over troposcatter paths, selective fading will be encountered with resultant transmission impairments, depending on the modulation method. An analysis has been made in a companion paper of such selective fading, based on an idealized model of troposcatter paths. It indicated that selective fading will be accompanied by phase nonlinearity which in a first approximation can be regarded as quadratic over a narrow band. A probability distribution for such quadratic phase distortion was derived. On the premise of quadratic phase distortion, the error probability owing to selective fading was determined for digital transmission by various methods of carrier modulation. The same idealized model and basic premise of quadratic phase distortion is used here to determine intermodulation distortion in FM for a signal with the statistical properties of random noise. An approximate expression for intermodulation noise owing to specified quadratic phase distortion has been derived, applying for any method of frequency pre-emphasis in FM. In turn, median intermodulation noise as well as the probability distribution of intermodulation noise has been determined, as related to certain basic system parameters. A comparison is made of predicted with measured intermodulation noise in four troposcatter systems with lengths from 185 to 440 miles. The results indicate that phase nonlinearity owing to selective fading can be approximated by quadratic phase distortion, or linear delay distortion, over an appreciable part of the transmission band ordinarily considered for troposcatter systems, with a probability distribution that can be determined from certain basic parameters of troposcatter links, such as the length and antenna beam angles. However, to predict intermodulation distortion on any system, further experimental data than are now available are required on beam broadening by scatter. The present random multipath FM distortion theory is shown to afford