Researchers Define Optogeometric Factor, Linking Étendue to Minimal Signal to Noise Ratio

The fundamental limit of signal detection in imaging systems has long been a subject of intense study, and new research clarifies this limit by connecting a key optical property to the underlying statistics of light. Jan Sova and Marie Kolaříková, both from Czech Technical University in Prague, lead a study that interprets the optogeometric factor, a measure of a detector’s light-gathering ability, as the number of optical modes a pixel can access. This innovative perspective establishes a direct relationship between how much light a detector collects and the inherent randomness of photon arrival, ultimately allowing the researchers to estimate the lowest possible signal-to-noise ratio achievable in an imaging system. The resulting formulas reveal how factors like lens aperture, pixel size, and even the temperature of the observed scene influence this fundamental noise limit, providing a benchmark for evaluating and improving imaging technology.

This innovative approach establishes a link between radiometric throughput and the statistical behaviour of photons, allowing for a deeper understanding of the limitations of imaging systems. Researchers combined established principles of quantum optics and radiometry to derive a new estimate of the lowest achievable signal-to-noise ratio (SNR) at the pixel level, providing a benchmark for evaluating imaging performance. The method involves analysing how the optogeometric factor, combined with the Bose-Einstein distribution, dictates the minimal SNR attainable given specific system parameters.

The team developed formulas to calculate this minimal SNR, considering factors such as aperture geometry, pixel pitch, f-number, wavelength, and source temperature, offering a comprehensive model for predicting system limitations. These calculations reveal that the minimal SNR is intrinsically linked to the number of optical modes a pixel can access, with a larger number of accessible modes generally leading to a lower achievable SNR, dictated by fundamental quantum statistics. Researchers demonstrate that the lowest possible SNR occurs in the case of thermal sources exhibiting maximum entropy in their photon statistics, representing a fundamental limit. Importantly, the method accounts for non-thermal sources, such as lasers or engineered photon states, which exhibit reduced entropy and consequently achieve higher SNR values, as their photon statistics deviate from the Bose-Einstein limit. This allows for a precise comparison between different illumination schemes and their impact on image quality. By providing a physically transparent benchmark, the approach enables scientists to evaluate imaging systems against the fundamental noise limit imposed by quantum mechanics, facilitating the development of more sensitive and efficient detectors.

Optogeometric Factor Quantifies Single-Pixel Light Gathering

Researchers have established a fundamental connection between a detector’s ability to gather light and the underlying principles of quantum optics, revealing how many independent “modes” of light a single pixel can actually capture. The team discovered that the optogeometric factor, a measure of a detector’s spatial angular throughput, directly corresponds to the number of accessible optical modes per pixel, effectively quantifying the pixel’s light-gathering capacity in quantum terms. This innovative approach bridges classical radiometry with quantum mechanics at the scale of a single detector element, a connection previously established only for entire imaging systems. The findings demonstrate that the optogeometric factor can be used to calculate the minimum achievable signal-to-noise ratio at the pixel level, providing a benchmark for evaluating imaging sensor performance against theoretical limits.

By linking the geometric throughput of a pixel to the number of quantum oscillators it can support, scientists can now precisely determine how many independent spatial-angular modes each pixel admits. Experiments reveal that a representative long-wave infrared (LWIR) pixel, with a pixel pitch of 17 μm and an f-number of 1. 0, exhibits an optogeometric factor of approximately 2. 27 x 10 -10 m 2 sr. At a wavelength of 10 μm, this translates to approximately 2.

27 independent modes per pixel, indicating that even in this scenario, the number of accessible modes is limited. The data confirms that when the optogeometric factor is less than one, the detector effectively admits only a fraction of a single mode, highlighting the importance of maximizing light throughput for optimal sensitivity. This pixel-based reformulation, absent in prior literature, provides a practical benchmark for designing and evaluating real imaging sensors, where sensitivity is ultimately limited by the finite number of optical modes each pixel can capture.

Geometric Limits to Pixel Signal-to-Noise Ratio

This work reinterprets the optogeometric factor as a measure of accessible optical modes per pixel, establishing a direct link between a pixel’s étendue and the underlying quantum degrees of freedom. By connecting this factor to the Bose-Einstein distribution, the research derives an estimate for the lowest achievable signal-to-noise ratio at the pixel level, providing a fundamental benchmark for imaging system performance. The resulting formulation unifies classical radiometry with quantum optics, clarifying the role of geometry in photon detection and offering criteria for evaluating and designing future imaging systems. The findings demonstrate that the minimal signal-to-noise ratio is influenced by aperture geometry, pixel pitch, f-number, wavelength, and source temperature, with longer wavelengths generally improving performance. Importantly, the research highlights that thermal radiation represents a maximum-entropy case, setting a lower limit on achievable signal-to-noise ratios, while non-thermal sources may achieve higher ratios due to reduced entropy.