Heterodyne Efficiency Research Articles

Measurement of the sensitivity of heterodyne detection to aberrations using a programmable liquid-crystal modulator

Heterodyne detection is known to be highly sensitive to wavefront distortions. However, quantitative measurements of the effects of aberrations are not easy to obtain. We propose to use a liquid-crystal spatial light modulator as a programmable wavefront aberrator. This allows us to simulate experimentally a coherent detection system at λ=632.8 nm. Two frequency-shifted plane waves (backscattered signal and local oscillator) are generated. The programmable liquid-crystal wavefront aberrator is used to computer-control the phase of the backscattered signal, and the heterodyne efficiency is measured. We present experimental measurements of the field-of-view, the effect of defocus and the sensitivity to atmospheric perturbations. In all three cases, the experimental data are compared to the theoretical predictions.

Modeling heterodyne efficiency for coherent laser radar in the presence of aberrations

Heterodyne efficiency of a coherent lidar system reflects the matching of phase and amplitude between a local oscillator (LO) beam and received signal beam and is, therefore, an indicator of system performance. One aspect of a lidar system that affects heterodyne efficiency is aberrations present in optical components. A method for including aberrations in the determination of heterodyne efficiency is presented. The effect of aberrations on heterodyne efficiency is demonstrated by including Seidel aberrations in the mixing of two perfectly matched gaussian beams. Results for this case are presented as animations that illustrate the behavior of the mixing as a function of time. Extension of this method to propagation through lidar optical systems is discussed.

Heterodyne Efficiency for a Coherent Laser Radar with Diffuse or Aerosol Targets

Abstract The performance of a coherent laser radar is determined by the statistics of the coherent Doppler signal. The heterodyne efficiency is an excellent indication of performance because it is an absolute measure of beam alignment and is independent of the transmitter power, the target backscatter coefficient, the atmospheric attenuation, and the detector quantum efficiency and gain. The theoretical calculation of heterodyne efficiency for an optimal monostatic lidar with a circular aperture and Gaussian transmit laser is presented including beam misalignment in the far-field and near-field regimes. The statistical behaviour of estimates of the heterodyne efficiency using a calibration hard target are considered. For space-based applications, a biased estimate of heterodyne efficiency is proposed that removes the variability due to the random surface return but retains the sensitivity to misalignment. Physical insight is provided by simulation of the fields on the detector surface. The required detector calibration is also discussed.

Characterization of pulsed coherent Doppler LIDAR with the speckle effect

The relationships among heterodyne efficiency γ, number of speckle cells M, and the ratio of receiver area to coherence area S(R)/S(C) for a pulsed coherent laser radar (CLR) are written through the use of mutual coherence functions. It is shown that numerical values for S(R)/S(C) that follow Goodman's definition [J. W. Goodman, in Laser Speckles and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 9-75] or that are obtained through the use of a transverse-field coherence length agree. In the frame of the Gaussian model proposed by Frehlich and Kavaya [Appl. Opt. 30, 5325 (1991)] a new equation is derived: M = (1 + S(R)/S(C)). This equation agrees with our experimental results. Our theoretical analysis shows that the number of speckle cells for an optimal monostatic CLR system is M ~ 4. An experiment has been conducted with a ground-based pulsed CO(2) LIDAR and remote hard targets to study the probability density function of LIDAR returns as a function of M and to study the dependence of M on S(R)/S(C). An assessment of CLR performance through the use of M or the collecting aperture S(R) is discussed.

Interference-phase measurement on a wavy air-water interface by using Fourier transform: application to coherent detection

Describes an experimental method, using Michelson interferometry and Fourier transform, to determine phase variations on wave fronts after double passage through a wavy air-water interface. The authors consider the statistical aspect of the wavefront deformations by using the averaged Fourier spectra over many independent realizations. The spreading of Fourier spatial spectra obtained from interferometric images can be used to determine heterodyne efficiency in airborne hydrographic systems using optical coherent detection.

Wave-front matching measurement in coherent CO_2 laser-radar

Wave-front matching of the local oscillator beam and the signal beam is of vital importance in optical heterodyne efficiency. A method for aligning the local oscillator beam and the signal beam is described. Mixing efficiency is improved. One can directly observe the matching procedure on an oscilloscope.

Heterodyne efficiency for a partially coherent optical signal

Heterodyne efficiency is discussed for a partially coherent signal and a coherent local oscillator beam. Both fileds are assumed to have Gaussian amplitude distributions. An input aperture is used to reduce the background noise. As the coherence of the signal decreases, the efficiency also decreases. However, there is a simple relation between the beam parameters and the detector dimensions to maintain optimum efficiency. The effect of the offset of the signal from the detector axis is also discussed, assuming the Gaussian probability of the deviation. In this case, the optimum parameters that give the maximum efficiency change with the average deviation.

Optimal truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscatter target

Two earlier computations of the optimal truncation of Gaussian beams for a simple, focused, coherent lidar that used an incoherent backscatter target with identical circular transmitter and receiver apertures differ because they refer to different receiver geometries. The definitions of heterodyne and systemantenna efficiencies are reviewed in light of the discrepancy and are used to compare the optical performance of systems with apertures illuminated by beam profiles that are not Gaussian. The heterodyne efficiency is less than 0.5 for all cases considered here.

Coherent laser radar performance for general atmospheric refractive turbulence

The signal-to-noise ratio (SNR) and heterodyne efficiency are investigated for coherent (heterodyne detection) laser radar under the Fresnel approximation and general conditions. This generality includes spatially random fields, refractive turbulence, monostatic and bistatic configurations, detector geometry, and targets. For the first time to our knowledge, the effects of atmospheric refractive turbulence are included by using the path-integral formulation. For general conditions the SNR can be expressed in terms of the direct detection power and a heterodyne efficiency that can be estimated from the laser radar signal. For weak refractive turbulence (small irradiance fluctuations at the target) and under the Markov approximation, it is shown that the assumption of statistically independent paths is valid, even for the monostatic configuration. In the limit of large path-integrated refractive turbulence the SNR can become twice the statistically independent-path result. The effects of the main components of a coherent laser radar are demonstrated by assuming untruncated Gaussians for the transmitter, receiver, and local oscillator. The physical mechanisms that reduce heterodyne efficiency are identified by performing the calculations in the receiver plane. The physical interpretations of these results are compared with those obtained from calculations performed in the target plane.

Heterodyne efficiency of quadrant photodetectors

In this paper we compare quadrant heterodyne efficiencies. Differences in efficiencies between circular and square detectors are small while relative spacing between quadrants is more important in its effect on efficiencies. Spot size relative to detector size is also important. The effect of angular misalignment on efficiency is smallest for the Airy-Airy combination.

Effects of tilt and offset of signal field on heterodyne efficiency

The effects of tilt and offset on the heterodyne efficiency are discussed for optical fields with Gaussian field distributions. An aperture is used in the input plane of the system to decrease the background noise which is incident on the signal. The numerical results show that in optimum conditions of the system and beam fields, the tilt must be less than ~10(-4) deg and the offset about one-fifth of the input aperture to obtain more than 60% of the ideal values of the efficiency.

Speckle Effects On Coherent Laser Radar Detection Efficiency

Equations for laser radar heterodyne efficiency are derived by assuming that heterodyne detection is degraded by phase-front distortion produced by target speckle and atmospheric turbulence. These equations are numerically evaluated for representative target detection scenarios to illustrate the effects of laser speckle on coherent laser radar detection.

Maximum heterodyne efficiency of optical heterodyne detection in the presence of background radiation

Maximum heterodyne efficiency is obtained for an optical heterodyne detection system in the presence of background radiation. When the local oscillator (LO) power is limited, the signal-to-noise ratio in the output is degraded from that of quantum-noise-limited detection by the background radiation noise. To reduce it, an aperture is used in front of the detector. The optimum incidence conditions of the signal and the corresponding maximum heterodyne efficiency are obtained numerically assuming that the signal and the LO fields are determinable and have Gaussian amplitude distributions. The spontaneous emission from the laser amplifier located just in front of the system is taken into account as the background radiation.

Heterodyne detection SNR: calculations with matrix formalism

A new method for calculating the heterodyne efficiency of an optical receiver is applied to specific optical systems looking through a turbulent atmosphere. The optical and atmospheric parameters which characterize the system efficiency are considered, and optimization of the performance of an heterodyne receiver is discussed.

Signal-to-noise ratio of heterodyne detection: matrix formalism

A matrix method is developed for calculating the heterodyne efficiency of an optical receiver, taking into account the local oscillator field distribution, the receiving optics, and the atmospheric turbulence. The heterodyne efficiency in a circular symmetric receiver is given by a product of several matrices, each representing one of the optical parameters of the system, such as defocusing, Fresnel number of the optical system, central obscuration, or atmospheric coherence radius.

Diffraction of a Gaussian beam through a finite aperture lens and the resulting heterodyne efficiency

The diffraction field of a Gaussian beam through a finite aperture lens is investigated. The field distributions at the position where the field is most focused are shown and compared with those obtained by an infinite aperture lens. The results are applied to an optical heterodyne detection system with Gaussian fields, and the optimum conditions that maximize the heterodyne efficiency are obtained numerically.

Optical heterodyne detection of an airy signal field with a gaussian local‐oscillator field

AbstractThe heterodyne efficiency in the optical heterodyne detection of an Airy signal field with a Gaussian local–oscillator field is analyzed with consideration of the effect of wavefront of both fields. The analysis is made for the case where both fields are normally incident on the detection plane. The beam parameters of the local oscillator field which maximizes the heterodyne efficiency are derived for given signal field. When the detection plane radius Γ0 is very large, the effect of the wavefront becomes apparent as F increases for given less aperture and as the effective aperture decreases for given F. The effect of finiteness of the detection plane on the heterodyne efficiency is investigated numerically. The maximum heterodyne efficiency is obtained when Γ0 = 1.13Fλ. The deterioration of the heterodyne efficiency in cases of oblique and off‐axis incidences of the local oscillator field is examined numerically.

Signal-to-noise ratio in optical heterodyne detection for Gaussian fields

The signal-to-noise ratio of optical heterodyne detection is discussed for Gaussian fields. The ratio of the aperture radius a of the detector to the smallest spot size w(s) of the signal has serious effects on the SNR. The conditions that maximize the SNR are obtained for a given signal or local oscillator field. The effects of field mismatching or misalignment are also discussed. Numerical analyses show that when such mismatching or misalignment exists, the spot size of the local oscillator field should be larger than that of the signal with a ratio of a/w(s) approximately 1.2. Then the heterodyne efficiency is rather insensitive to the errors and yet takes reasonable values (above 0.8).

Rayleigh light scattering from concentrated solutions of polystyrene in cyclohexane

The Rayleigh light scattered at 90° by concentration fluctuations in solutions of polystyrene with cyclohexane, in the mass concentration range 0.18–0.56 of polymer, is observed to mix with a heterodyne efficiency close to unity with light scattered elastically by dust particles. A technique is described where by using a digital photon correlator the absolute intensity of the Rayleigh light is measured and the elastic modulus of the uncross-linked polymer gel deduced. The results are in satisfactory agreement with values found in the literature. The measurements of the relaxation time of the concentration fluctuations allow the friction constant between the solvent and the polymer matrix to be calculated.

Statistics of a Geometric Representation of Wavefront Distortion

A precise statistical definition is established for the geometric “shape” of a randomly distorted wavefront. Relationships between the phase-structure function and the statistics governing the shape are derived. The most significant portion of wavefront distortion caused by atmospheric turbulence is a random tilting of the plane-wave front. A procedure is outlined for calculating the influence of wavefront distortion on optical systems. Estimates are formed of the effect of wave-front distortion on photographic resolution and optical heterodyne efficiency.