Empirical compensation of reciprocity failure and integration time nonlinearity in a mid-wave infrared camera

Abstract

Thermal-infrared radiation measurements, conducted using an InSb camera, indicated a failure of the reciprocity law for a wide range of radiation intensities and integration times. When reciprocity between radiation flux and integration time was assumed, the radiation estimates, computed from different combinations of output signals and selected integration time values, suffered from imprecisions of up to 12%. Temperature errors of ~4% were predicted for low emissivity surfaces, at all temperatures. A novel empirical methodology, which compensates for multiple nonlinearity effects, is presented. Among different types of models, it is demonstrated that an equation, which represents a power-law dependence of the output signal on integration time best describes the physical system. Experimental procedures are suggested to avoid nonlinearity-related errors.

Quantitative image fusion in infrared radiometry

“…This work uses the latter. In order to normalize the response of one pixel to another, equations (7) and (8) can be combined to yield…”

“…Similarly, when NUC-IT is used, coefficient dependence on integration times must not occur. In reality, although the bias frame components can be considered fixed, the pixel responsivity is known to be a nonlinear function of both R and IT [7,26]. In recent works, attempts have been made to reduce this linearization error by using more than two reference points with piecewise-linear functions [27], higher order polynomials [28] and other nonlinear schemes [29].…”

“…where A = 14 583, B = 4144, and C = 6.299 (setup-specific fitted constants) and T is the radiometric temperature of a black body in (K) [7,14]. The resulting R value is multiplied by the emissivity map, and the dark frame is superimposed.…”

“…In the scope of motion detection in video streams, image subtraction is usually called 'background subtraction' and is done using a subtrahend image of a static scene [6]. In contrast, when the subtrahend image is taken with a closed shutter (or any equivalent method of blocking the incoming radiation), the procedure is known as 'dark-frame subtraction', which improves radiance estimates in individual IR images [7]. A dark frame taken at an integration time close to zero is called a bias frame (BF), and is often used to compensate for the constant offset contribution of the FPN.…”

“…Thereby, the different response curves of all pixels ideally collapse onto a single function. In reality, the implicit linearity assumption of detector response (which forms the so-called 'reciprocity law') is not satisfactory for quantitative measurements [7,[10][11][12]. Even when the NUC coefficients are sufficient approx imations for a specific signal range, they need to be readjusted due to changes in scene flux and the slow time-dependent drift (order of days) in FPN.…”