Spatial aliasing quantification and sampling frequency selection in imaging sensors.

Sampling, whether it be spatial or temporal, is a common occurrence. A result of this fact is the need for an anti-aliasing filter, which effectively limits high frequencies and prevents them from folding over and appearing as a low(er) frequency when sampled. In typical imaging sensors, such as optics plus focal plane detector(s), the optical transfer function (OTF) acts as a spatial anti-aliasing filter. However, decreasing this anti-aliasing cutoff frequency (or lowering the curve in general) via the OTF is tantamount to image degradation. On the other hand, the lack of high-frequency attenuation produces aliasing within the image, which is another form of image degradation. In this work, aliasing is quantified, and a method for sampling frequency selection is brought forth.

Back-of-the-envelope image resolution estimation using an aberrated Rayleigh criterion.

In an optical imaging sensor (i.e., lens plus focal plane array), the critical output is the image itself, and quality of that image is a measure of the sensor's performance. Image quality is dependent on several terms such as the sensor-level point-spread function (PSF), sampling period, and signal-to-noise ratio. The sensor resolution is mainly dependent on the PSF, which is comprised of many aspects. Often, the resolution is determined by the diffraction-limited Rayleigh criterion; however, due to the blur contributions of the collecting optics wavefront errors, pixel size, etc., the sensor PSF is not often diffraction-limited. Here, we develop two simple back-of-the-envelope calculations that provide an estimate of a nondiffraction-limited imaging sensor PSF size based on the sensor-level required resolution. Moreover, an allocation based on this PSF size can be used to dole out an allotment to the various blur effects, e.g., wavefront error, during sensor-level design.

Wavelength selection approach for an incoherent optical detection sensor (LiDAR).

An energy or direct detection or time-of-flight sensor (a type of incoherent optical detection sensor) used for remote detection and ranging purposes is a useful measurement tool due to its simplicity and high performance in uncluttered environments. A sensor- or top-level design approach has been established [Appl. Opt.59, 1939 (2020)APOPAI0003-693510.1364/AO.384135] due to the usefulness of these sensors, and with this, lower-level designs can be performed to optimize the sensor for particular applications. A critical design element of an incoherent optical detection sensor, or any active optical sensor for that matter, is the selection of a best or optimal central operational wavelength. First and foremost, a relevant metric is developed to provide an optimum wavelength. Then, a search for this wavelength is generated given a generic set of components where conditions are best suited for direct detection sensors, i.e., uncluttered environments or space-like, and finally, the search is again carried out for conditions within the Earth's atmosphere where transmission plays a role.

Designing an incoherent optical detection sensor (LiDAR) utilizing a range-compensating lens.

There are many trades to be made when designing an optical system. In this work, an incoherent optical detection sensor (often referred to as an energy- or direct-detection sensor, or a time-of-flight LiDAR) is designed at the sensor or top level using newly developed tools [Appl. Opt.59, 1939 (2020)APOPAI0003-693510.1364/AO.384135]. While incoherent detection sensors, relative to coherent frequency or phase-modulated sensors, are not as useful in cluttered environments, they have their place due to their simplicity and high performance in uncluttered or lightly cluttered environments. In this particular design, a nontraditional receive lens is utilized that has the unique ability to adjust the amount of return signal placed on the detector based on target range, i.e., a range-compensating lens (RCL) [Appl. Opt.58, 7921 (2019)APOPAI0003-693510.1364/AO.58.007921]. Only a two-element RCL is utilized in this work, but it proves the ability to shape the return signal gauging the changes in the stochastic performance, paving the way to a multi-element RCL for additional design freedom in shaping.

Specular signal return through a range-compensating lens.

A range-compensating lens has been developed which alleviates, to a certain degree, the one-over-range-squared attenuation in the signal (laser) return for active optical systems [Appl. Opt.58, 7921 (2019)APOPAI0003-693510.1364/AO.58.007921]. This compensation applies to the diffuse return and, in particular, the perfectly diffuse return that is an assumption used to develop the equations. However, there is another component of the return that is equally important, and that is the specular signal return. Often this return is a result of a very shiny and close target, since the return needs to closely follow the outgoing beam path in order for the light to be returned to the detector. This implies a high sensitivity to target orientation. For this reason, specular returns are not counted on as a signal return, and the sensor is generally not designed to use this type of return, which can lead to an undesired detector saturation, should a high reflectivity specular return occur. This return, with respect to a range-compensation lens, was only discussed briefly and qualitatively. The work here means to address this specular signal return quantitatively as it applies to a range-compensating lens as compared to that of a traditional lens and considers the specular performance on the sensor-level.

Incoherent detection sensor design approach using Gaussian optics.

An incoherent optical detection sensor (often referred to as energy or direct detection sensor) used for remote detection and ranging purposes is a useful tool. While the accuracy and robustness of an incoherent sensor relative to a coherent sensor may be lacking particularly in cluttered environments, it has a place in the world due to its simplicity and performance. With this, a best design approach is sought to meet requirements in a stochastic fashion. In developing the design approach, motivations are borrowed from decades of research in radar systems. This article provides a sensor- or top-level design approach for an incoherent optical detection sensor based mainly on paths developed in radar.

Back-of-the-envelope image quality estimation using the national image interpretability rating scale: erratum.

This paper corrects several errata in Appl. Opt.58, 6586 (2019)APOPAI0003-693510.1364/AO.58.006586.

Range-compensating lens for non-imaging active optical systems.

In many active optical systems where the light is supplied, such as a range finder or optical radar, there is a possibility that the detector (pixel) can be destroyed if significant signal is returned or at the very least blinded for a period of time. This is because the designer struggles with the "one over range squared" loss, which can amount to significant attenuation in the return signal, given the range requirements. When pushing the range limit requirement, the sensor is in need of a large dynamic range detector and/or some form of detector protection when the target is quite close. There is then a search for a range-compensating lens. This work proposes a lens that attempts to compensate for range signal loss passively and instantaneously by combining lens elements in parallel rather than in series, as is typically done. The proposed lens is relatively simple, compensates for range, albeit not perfectly, and has its own drawbacks.

Back-of-the-envelope image quality estimation using the national image interpretability rating scale.

For an optical imaging system, the critical output is the image itself, and therefore, the quality of that image is of utmost importance. To estimate or predict the image quality (IQ), a simulation/model is typically created to yield an output image, given an imaging system and an object/scene. The IQ is typically graded based on the imaging system along with the scene. Developing an imaging simulation and creating input scenes to produce IQ results can be time-consuming, leading to a desire for a simple method to estimate the predicted IQ. This work develops a national image interpretability rating scale (NIIRS) IQ value based on simplifying assumptions for remote-sensing purposes. While the results are on the optimistic side, this back-of-the-envelope IQ estimation allows the process of developing a new imaging system to move forward more in parallel rather than in series, i.e., developing an imaging full simulation/model in parallel with designing/procuring hardware.

Polarimetric characterization of birefringent filter components.

Over the past 75 years, birefringent filter technology has evolved significantly. For nearly that same period of time, these filters have been designed and used by solar scientists to study the Sun. Prior to assembling these types of filters, each component, e.g., polarizers and wave plates, is characterized to determine its polarimetric parameters to ensure the desired filter design performance. With time and cost becoming an ever increasing issue, it is imperative to test components designated for a birefringent filter efficiently. This article addresses a shift to increased efficiency when testing components of very low volume (<5 units) solar research filters that minimizes high-priced hardware expenditures, i.e., Mueller matrix spectropolarimeter.

In situ calibration of tunable filters: Lyot and Michelson.

Solar imaging optical filter technology has progressed significantly over the past 75 years, and the ability to tune narrowband filters is particularly valuable for solar atmosphere sensing. For example, imaging while tuning over a narrow solar spectral line (emission or absorption) provides two-dimensional measurements of Doppler shifts and magnetic fields. While tuning ability has improved significantly, tuning accuracy can be a challenge over time given system actuator drifts. For many cases, the ability to calibrate these actuators in situ is convenient and cost effective (e.g., ground-based observatories), and for other cases it is required (e.g., in a spacecraft). It is ideal to calibrate in situ without the need for additional hardware such as a spectrometer, and if that cannot be achieved, the next best thing is to do so with minimum additional hardware. Two examples of solar filters that need to be calibrated periodically are: (1) a liquid crystal variable retarder Lyot filter and (2) a tunable Michelson interferometer. For the first, the filter can have a number of stages back-to-back to achieve the desired finesse. Within each stage there is a liquid crystal variable retarder that adds some amount of retardance to the stage's fixed birefringent crystal; this provides wavelength bandpass tuning. For the second, there can be several Michelson interferometers in series each with an actuator to adjust the optical path length in one of its optical paths for tuning. The stacking of these filters implies there is a need to calibrate more than one actuator. An algorithm has been developed to calibrate these types of stacked and nonstacked filters in situ with minimal, if any, hardware additions.

Real time polarimetric dehazing.

Remote sensing is a rich topic due to its utility in gathering detailed accurate information from locations that are not economically feasible traveling destinations or are physically inaccessible. However, poor visibility over long path lengths is problematic for a variety of reasons. Haze induced by light scatter is one cause for poor visibility and is the focus of this article. Image haze comes about as a result of light scattering off particles and into the imaging path causing a haziness to appear on the image. Image processing using polarimetric information of light scatter can be used to mitigate image haze. An imaging polarimeter which provides the Stokes values in real time combined with a "dehazing" algorithm can automate image haze removal for instant applications. Example uses are to improve visual display providing on-the-spot detection or imbedding in an active control loop to improve viewing and tracking while on a moving platform. In addition, removing haze in this manner allows the trade space for a system operational waveband to be opened up to bands which are object matched and not necessarily restricted by scatter effects.

Signal, noise, and bias for a broadband, division-of-amplitude Stokes polarimeter.

We analyze estimation error as a function of spectral bandwidth for division-of-amplitude (DoAm) Stokes polarimeters. Our approach allows quantitative assessment of the competing effects of noise and deterministic error, or bias, as bandwidth is varied.We use the signal-to-rms error (SRR) as a metric. Rather than calculating the SRR of the estimated Stokes parameters themselves, we use the singular-value decomposition to calculate the SRRs of the coefficients of the measured data vector projected onto the measurement matrix left singular vectors.We argue that calculating the SRRs for left singular vector coefficients will allow development of reconstruction filters to minimize Stokes estimation error. For the example case of a source with constant polarization over a relatively wide band, we show that as the spectral filter bandwidth is increased to include wavelengths significantly different than the design wavelength, the SRRs of the estimated left singular vector coefficients will a.) increase monotonically if relatively few photo-detection events (PDEs) are recorded, b.) after a sharp peak close to the design wavelength, decrease monotonically if relatively many PDEs are recorded, and c.) have well-defined maxima for nominal PDE counts. Given some idea of the source brightness relative to detector noise, one can specify a spectral filter bandwidth minimizing the variance and bias effects and optimizing Stokes parameter estimation. Our approach also allows one to specify the bandwidth over which the response of "achromatic" optics must be reasonably invariant with wavelength for rms Stokes estimation error to remain below some desired maximum. Finally, we point out that our method can be generalized not only to other types of polarimeters, but also to any sensing scheme that can be represented by a linear system for limiting values of a certain parameter.