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

Abstract

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.

Spatial aliasing quantification and analysis of existing imaging sensors: NASA’s Hubble Space Telescope, OrbView-3 OHRIS, and commercial-off-the-shelf camera for autonomous robots

“…The full mathematical details behind the aliasing error are available in Ref. 7, and only the key results are provided here keeping this work relatively self-contained. The aliasing error (ϵ) is a function of the aliasing quantity (α) and is ϵ=|1−α|.…”

“…For imaging sensors, the input is the object or, more specifically, the object spectrum and is typically a broad-band spatial spectrum—common for sensor systems. If the system has a broad-band input and an anti-aliasing filter [for imaging sensors, this is the optical transfer function (OTF)], which attenuates the high frequencies and (possibly) has a high frequency cut-off, then the Nyquist–Shannon sampling theorem should be considered more of a maximum sampling frequency and not a minimum, 7 and the differences in the sampled image with respect to the unsampled or truth image, an aliasing error, has been quantified for imaging sensors 7 . This computed aliasing error not only shows up in a visual inspection of the sampled image but also when the sampled image is sent to a neural network, which can represent a convolution operation amongst others, 8 – 10 and recognizing this fact makes aliasing even more critical for many end-to-end imaging systems.…”

“…In addition, the concepts provided here and in Ref. 7 apply to any sensor or sampling system whether it be an imaging sensor or a sensor that collects any data in any of the three spatial directions or the temporal.…”

“…Applying the aliasing error developed in Ref. 7 to currently existing imaging sensors is the focus of this work. The aim is to appreciate how well existing systems are sampled to better inform how future systems could potentially be improved by trading aliasing error and sampling frequency given existing imagery.…”

“…The objects employed are the same two somewhat bounding object spectra used in Ref. 7 and are provided in Fig. 1: (1) 1(σ) unity over all frequencies (white) representing a point source object in the spatial domain with a significant amount of high frequency content is similar to viewing a distant star common in astronomy and used in sensor alignment, 11 and (2) an extended object given as an inverse or reciprocal frequency spectrum of Rβ,γ(σ)=C|σangσ0|β+γ,where C is an arbitrary constant value set to unity with units of the spectrum, σang is the angular spatial frequency in deg−1, σ0=1 deg−1, β and γ are tuning parameters set to 0.9 and 0.01, respectively, with γ preventing the spectrum from becoming undefined at zero frequency.…”