Sensor Models 2. Reading: Chapter 3. ECE/OPTI 531 Image Processing Lab for Remote Sensing Fall 2005

Transcription

1 Sensor Models Reading: Chapter 3 ECE/OPTI 53 Image Processing Lab for Remote Sensing Fall 25 Sensor Models LSI System Model Spatial Response Spectral Response Signal Amplification, Sampling, and Quantization Simplified Sensor Model Geometric Distortion Sensor Models 2 Fall 25

2 Overall Sensor Model Remote sensors are complex systems of optical, mechanical and electronic components These components determine the quality of the data from the sensor The sensor may be considered a black-box that converts at-sensor radiance to DNs Sensor Models 3 Fall 25 LSI System Model Model the various systems as Linear Shift- Invariant (LSI) A linear transformation of the input x results in a similar transformation of the output y Superposition principle If T[f ] = g and T[f 2 ] = g 2, then T[a f + a 2 f 2 ] = a g + a 2 g 2 Shifting the input results in a similar shift of the output Shift invariance If T[f(x)] = g(x), then T[f(x-x )] = g(x-x ) LSI model is generally applicable over the nominal range of operation for these systems Model will break down as performance limits are approached (i.e., system response becomes non-linear) Sensor Models 4 Fall 25 2

3 Instrument Response Any signal can be written as a sum of weighted delta functions using the sifting property What happens when this input form is put into a linear system? Knowing the transformation of a delta function, the impulse response, completely characterizes the LSI system Sensor Models 5 Fall 25 Instrument Response (cont.) The precision of measurement is determined by the instrument response, r The transformation from the input physical quantity to the measurement is described mathematically by a convolution where i(α) is the input signal, a function of time, space, etc. r(z -α) is the instrument response, inverted and shifted by z o(z ) is the output signal at z = z W is the range over which the instrument response is significant Shorthand notation, o(z) = i(z) r(z), read as the output signal is the input signal convolved with the instrument response. Sensor Models 6 Fall 25 3

4 -D Convolution Example Input and Impulse Response Convolution Operation The measured value at z is an average of the input signal in the vicinity of z, weighted over the range W by the instrument response Output Sensor Models 7 Fall 25 Resolution Any instrument that measures a physical quantity is limited in the amount of detail it can capture This limit is referred to as the instrument s resolution Resolution is a term that is widely used, but often misunderstood The width W of the instrument response defines the spatial resolution, or effective GIFOV Sensor Models 8 Fall 25 4

5 Sensor Models LSI System Model Spatial Response Spectral Response Signal Amplification, Sampling, and Quantization Simplified Sensor Model Geometric Distortion Sensor Models 9 Fall 25 Spatial Response The spectral signal is convolved with the sensor spatial response where the spatial response of an imaging system is now called the Point Spread Function (PSF) The net sensor PSF is a convolution of individual responses from: optics PSF opt image motion PSF IM detector PSF det (defines the geometrical GIFOV) electronics PSF el Sensor Models Fall 25 5

6 PSF Properties The net sensor PSF is wider than the GIFOV because of PSF opt in both directions PSF IM cross-track for whiskbroom scanners in-track for pushbroom scanners PSF el cross-track for whiskbroom scanners Reasonable assumption in many cases is that the PSF is separable in the cross-track and intrack directions Sensor Models Fall 25 PSF Comparison normalized detector PSF det significant out-of-pixel response in all four systems in-track 2 3 cross-track x -4 AVHRR 8 6 x -4 MSS x -3 x -4.8 SPOT HRV 8 6 TM Sensor Models 2 Fall 25 6

7 Sensor Models LSI System Model Spatial Response Spectral Response Signal Amplification, Sampling, and Quantization Simplified Sensor Model Geometric Distortion Sensor Models 3 Fall 25 Spectral Response The at-sensor radiance is transferred to the sensor image plane by the camera equation where τ o (λ) is the optics spectral transmittance N is the optics f-number, given by the ratio of the optical focal length divided by the aperture stop diameter the optical magnification is assumed to be one The spectral responsivity R b (λ) weights the image plane irradiance to yield a signal value Sensor Models 4 Fall 25 7

8 Spectral Response (cont.) Spectral responsivities are not ideal rectangular bands (Fig. 3 8) AVHRR Relative Response AVHRR AVHRR2 Relative Response AVHRR3 AVHRR4 AVHRR wavelength (nm) wavelength ( µm).8.8 TM Relative Response TM TM2 TM3 TM4 Relative Response TM5 TM wavelength (nm) wavelength (nm).8.8 SPOT Relative Response SPOT SPOT2 SPOT3 MSS Relative Response MSS MSS2 MSS3 MSS wavelength (nm) wavelength (nm) Sensor Models 5 Fall 25 Hyperspectral Responsivity Hyperspectral sensors have relatively constant spectral resolution across a wide spectral range Spectral band properties for AVIRIS (Fig. 3 9) 25 2 band center wavelengths linear with band number center wavelength (nm) 2 5 center wavelength bandwidth bandwidth (nm) average bandwidth about nm band 8.5 Sensor Models 6 Fall 25 8

9 Sensor Models LSI System Model Spatial Response Spectral Response Signal Amplification, Sampling, and Quantization Simplified Sensor Model Geometric Distortion Sensor Models 7 Fall 25 Signal Amplification The electronic signal produced by the detectors is amplified Some sensors have multiple gain settings, e.g. SPOT HRV (Chavez, 989) and ETM thermal band, to increase signal level for dark objects Linear amplification characteristics (Fig. 3 7) a b optional high gain b signal range required at A/D input for full range DN output standard gain b anticipated range of detected signals offset b low radiance scenes e b all scenes Sensor Models 8 Fall 25 9

10 Sampling and Quantization The amplified signal is sampled in time (during scan) and quantized into Digital Numbers (DNs) Quantization is a low-level noise superimposed on the data values For Q bits/pixel quantization there are 2 Q integer DNs over the range [...2 Q -] Radiometric resolution = 2 -Q Linear quantization transfer characteristics (Fig. 3 8) 2 Q DN input signal to A/D converter a b Sensor Models 9 Fall 25 Sensor Models LSI System Model Spatial Response Spectral Response Signal Amplification, Sampling, and Quantization Simplified Sensor Model Geometric Distortion Sensor Models 2 Fall 25

11 Effective Sensor Model Total measured signal at pixel p in band b where DN pb is the Digital Number at pixel p in band b L λ (x,y) is the at-sensor spectral radiance from scene location (x,y) K b is a gain coefficient for band b that includes sensor gain, detector spectral responsivity and spectral filter transmittance offset b is the sensor offset coefficient for band b the gain and offset are effective quantities, averaged over an effective spectral band Sensor Models 2 Fall 25 Gain-Offset Model The three integrals are over: the effective spectral response range of band b (spectral resolution) the effective spatial response range in-track and crosstrack (spatial resolution) Assume a band- and space-integrated at-sensor radiance L pb at pixel p, band b. Then, DNs are linearly proportional to the total at-sensor radiance Ignores radiometric quantization and nonuniform response within spectral bands and the GIFOV Simplifies modeling and radiometric calibration of the sensor Sensor Models 22 Fall 25

12 Sensor Models LSI System Model Spatial Response Spectral Response Signal Amplification, Sampling, and Quantization Simplified Sensor Model Geometric Distortion Sensor Models 23 Fall 25 Sources of Distortion All remote sensing images are distorted relative to a map platform motion, especially airborne sensors scanning distortion of the Ground Sample Interval (GSI) topography Distortion caused by airplane motion (ASAS airborne sensor) in-track ground distance (km) cross-track ground distance from nadir (km) cross-track pixel number orbital track Bow-tie distortion in AVHRR data (Fig. 3 23) Sensor Models 24 Fall 25 2

13 Scanning Distortion line and whiskbroom scanners (Fig. 3 22) f pushbroom scanners (Fig. 3 24) W f FOV FOV H "! H "! nadir! GSI f (!) nadir! GSI f (!) GSI e (!) GSI e (!) relative GSI flat earth true earth off-nadir scan angle (radians) Sensor Models 25 relative GSI flat earth true earth off-nadir view angle (radians) Fall 25 Topographic Relief Image offset proportional to elevation above base plane, or datum Stereo pair of images can be used to find elevation Imagery corrected for topographic distortion is called orthographic ground point at A actually appears to come from A because of topography A A Sensor Models 26 Fall 25 3