1. REMOTE SENSING Characteristics of Sensor Systems
Professor Ke-Sheng Cheng
Department of Bioenvironmental Systems Engineering
National Taiwan University

2. Outline The Electro-Optical Sensor Systems
Detector characteristics
Types of image sensing systems
Resolutions of Remote Sensors
Spatial resolution
Spectral resolution
Radiometric resolution
Temporal

3. The Electro-Optical Sensor Systems
Major elements of an electro-optical sensor system include
an optical sensing system which is composed of lenses, mirrors, apertures, modulators and dispersion devices,
detectors which convert the radiances reaching its surface to electrical signals,
a signal processor which transforms the electrical signal to desired output data.

4. Schematic diagram of a multispectral electro-optic sensor system

5. The optical sensing system receives radiances from the atmosphere and the Earth surface. The combination of lenses, mirrors, apertures, modulators and dispersion devices separates the total radiance into desired multispectral radiances.
These multispectral radiances reach the detectors and their EM radiation energy is converted to electrical signals (current or voltage) of the corresponding channels. The advent of high resolution Charged-Coupled-Device (CCD) has made CCD detectors most widely used for remote sensing.
Finally, the signal processor transforms the analogue electrical signals to discrete outputs based on predetermined transformation functions.

6. Detector characteristics
Modern remote sensing systems use detectors which yield output signals in the form of a measurable electrical signal (current or voltage).
There are two broad types of electro-optical detectors
thermal detectors
photon detectors

7. Thermal detectors
The thermal detectors absorb optical or infrared energy of incident photons, convert it to heat, and thus undergo a temperature rise.
The thermal detector can be used over the wavelength range of visible to thermal infrared since the temperature rise is dependent on the energy absorbed and not the photon wavelength directly.

8. Any energy which is absorbed causes a response in the detector
Any energy which is absorbed causes a response in the detector. Therefore, it is possible to use a thermal infrared detector at room temperature to detect radiation from room temperature blackbodies.
Thermal detectors need time to reach thermal equilibrium before they can provide an accurate measurement, their response to incident radiation tend to be slow, and thus, are not practical for most remote sensing applications.

9. Photon detectors
Photon detectors measure the rate at which individual photons interact with the detector. Photons incident on a photon detector interact directly with the electronic energy levels within the detector to produce free charge carriers.
Individual photons produce significant change in the detector material which in turn produces a change in the current or voltage in an external circuit. 

10. Since photon detectors do not rely on the conversion of incoming radiation to heat, but convert incoming photons directly into an electrical signal, photon detectors are sensitive to the amount of energy associated with each incident photon and have a high speed of response and are therefore are commonly used in remote sensing applications.

11. Performance of detectors is determined by characteristics of detectors including spectral responsivity, speed of response, signal-to-noise ratio (SNR), spectral detectivity, dynamic range of response, etc. Some of these parameters are defined and discussed as follows.

12. Responsivity
The responsivity is defined as the detector output per unit of input power. The units of responsivity are either volts/watt or amperes/watt, depending on whether the detector output is a voltage or electric current.

13. Let  be the radiant flux incident on the detector and V be the output of the detector. The responsivity can be expressed as:
For photon detectors, the responsivity depends on wavelength, and the term spectral responsivity is used.

14. Schematic illustration of the spectral responsivity curves of thermal and photon detectors

15. Since photon detectors rely on the action of photon to interact with electrons in the detector material and to generate free electrons, the incident photon must have sufficient energy to free an electron. Thus, a cutoff wavelength (c) appears in the spectral responsivity curves of photon detectors. Photons with wavelength longer than c do not have enough energy to free the electron and the detectors yield no response.

16. In remote sensing applications, incident radiant fluxes are often restricted to be within specific spectral bands (1, 2) and thus the detector output (V) and the bandpass responsivity (R) can be calculated by

17. The spectral responsivity is a fixed characteristic of the detector
The spectral responsivity is a fixed characteristic of the detector. However, for a given detector, the bandpass responsivity may vary with the spectral distribution of incident flux.

18. Signal-to-noise ratio (SNR)
There is uncertainty in the signal (voltage or current) level within a fixed period of time even when the detector is exposed to a constant level of photon flux.
The standard deviation of the signal level is defined as the photon noise (Nphoton) or shot noise.

19. Noise can also exist even when there is no incident flux at the detector. This may be due to fluctuations in detector dark current and readout-related noise.
The dark current is caused by thermally generated electrons in the detector system.
The read noise is mainly caused by thermally induced motions of electrons in the output amplifier.
To achieve a good performance of the detector, we would want the signal level to be sufficiently higher than the noise floor.

20. Fluctuation of the signal and noise levels

21. Variation of the signal level arises from the random arrival of photons on the detector surface.
The number of photons incident on the detector for a given period of time can be characterized as a Poisson distribution. The standard deviation of a Poisson distribution is equivalent to the square root of its mean value. Thus, the photon noise is numerically equivalent to the square root of the average signal level.
Similarly, the dark noise equals the square root of the average dark current.

23. The Signal-to-noise ratio (SNR) is defined as the mean signal level divided by the total noise, i.e.
Higher SNR values are desired to ensure good performance of detectors, and there are several ways to improve the SNR including
broadening the sampled wavelength bands
increasing the spatial resolution
increasing the dwell time for each pixel.

24. Noise equivalent power (NEP)
The noise equivalent power (NEP) is defined as the required radiant power incident on the detector that can produce an output voltage (or current) equivalent to the dark noise of the detector. By definition, the NEP (in watts) is expressed as

25. NEP is another way of quantifying the noise in terms of the minimum level or incident power that can be detected by the detector.
For a detector with measurement band (1, 2), the amount of noise is dependent on the bandwidth of the measurement and that bandwidth must be specified in expression of NEP, i.e.
I is the irradiance incident on the detector of area A, f is the frequency interval corresponding to measurement bandwidth =21.

26. From the definition, it is apparent that the lower the value of the NEP, the better are the characteristics of the detector for detecting a small signal in the presence of noise.
The NEP is dependent on the area of the detector. Since many detectors have NEP proportional to the square root of their area, another term called detectivity (D*) is defined by

27. D* is independent of the area of the detector and provides a measure of the intrinsic quality of the detector material itself, independent of the area with which the detector happens to be made.
A high value of D* means that the detector is suitable for detecting weak signals in the presence of noise.

28. Types of image sensing systems
Line scanner
A rotating scanner sweeps the ground along the cross-track direction.
The cross-track angular extent of the area swept by the system is called the field of view (FOV). Accordingly, the angular extent of the detector is referred to as the instantaneous field of view (IFOV).
The area projected on the ground by the scanner at any time instant is called the ground sample or ground instantaneous field of view (GIFOV).
The ground width of each scanning cycle is called the ground swath.

29. A line scanning system

30. If the scanning system is flying at an altitude of H, then GIFOV at nadir (the point perpendicularly under the sensor) can be calculated as
During each scan, the radiant energy from ground surface is sampled at a constant rate. The cross-track sampling rate and the scanning speed of the sensor together determine the ground sample interval (GSI) in the cross-track direction.

31. Similarly, the along-track GSI is determined by the combined effect of the along-track sampling rate and flying speed of the sensor.
Although a common practice is to design the image sensing system such that both GSIs (along-track and cross-track) equal the GIFOV, there are systems (e.g. Landsat MSS) that yield oversampling effect along the cross-track direction.

32. Effect of oversampling
Oversampling reduces the cross-track GSI, and thus yields an image of finer details. However, it should be noted that oversampling does not affect the GIFOV which is a characteristic of the detector by design.

34. Many line scanners also use a dispersing element to spectrally disperse incident light. A few discrete detectors or a linear array of detectors placed at the focal plane are then used to sample signals of individual spectral channels.
Such systems are known as the multispectral line scanners. Line scanners are mostly mounted on aircrafts.
Aircraft platforms and flying speed are usually not stabilized such that geometric distortions may occur from one line to the other, or even from pixel to pixel within a line.

35. Whisk-broom scanner
The line scanner design uses a single detector to sweep the ground line by line. As a result, the dwell time, the time span for the detector to scan over a ground sample, is usually very short.
In contrast, whisk-broom scanners employ an array of several detectors aligned in the along-track direction, resulting in improvement in dwell time.

36. Similar to the multispectral line scanners, multispectral whisk-broom scanners also use dispersing element and discrete or a linear array of detectors to sample signals of individual spectral channels.
The Landsat multispectral scanner (MSS) and Landsat Thematic Mapper (TM) are two examples of multispectral whisk-broom scanners.

37. A whisk-broom scanning sensor

38. Push-broom scanner
Unlike whisk-broom scanners which have discrete detectors aligned in the along-track direction, push-broom scanners have a linear array of detectors in the cross-track direction.
Instead of swing-scanning in the cross-track direction, the detectors move forward during flight without any swing movement.

39. A push-broom scanning sensor

40. The flying speed of the scanner system and the radiance sampling rate usually are designed in a way such that both the cross-track and along-track GSIs are numerically the same as the GIFOV.
The swath width (in number of pixels) of an image equals the number of detectors.

41. Area-array scanner
Framing-array scanners utilize a two-dimensional array of detectors to acquire the image of a frame-projected area on the ground (see Figure 2.5(c)), eliminating the distortions due to within-frame sensor motion.

42. An area-array scanning sensor

43. Outline The Electro-Optical Sensor Systems
Detector characteristics
Types of image sensing systems
Resolutions of Remote Sensors
Spatial resolution
Spectral resolution
Radiometric resolution
Temporal

44. Resolutions of Remote Sensors
In order for a remote sensor to collect and record energy reflected or emitted from a target area, it must reside on a stable platform.
Platforms for remote sensors may be situated on the ground, on an aircraft, or on a spacecraft or satellite.
The quality of remote sensing images acquired by theses sensors is affected by many factors including the orbit and speed of platforms and sensor characteristics.
Four types of resolutions which are pertinent to application of remote sensing images can be defined as follows.

45. Spatial resolution
Spatial resolution is a measure of the spatial detail in an image, which is a function of the design of the sensor and its operating altitude above the surface.
Each of the detectors in a remote sensor measures radiant energy received from an area within its ground sample. Thus, spatial resolution is most commonly expressed as the size of the ground sample.

46. The smaller the ground samples are, the more detailed will be the spatial information that we can interpret from the image.
Shape is one visual factor that we can use to recognize and identify objects in an image. Shape is usually discernible only if the objects are several times larger than the spatial resolution.
On the other hand, objects smaller than the spatial resolution of the image may be detectable in an image (Smith, 2006).

47. If such an object is sufficiently brighter or darker than its surroundings, it will dominate the averaged brightness of the image cell it falls within, and that cell will contrast in brightness with the adjacent cells.
We may not be able to identify what the object is, but we can see that something is present that is different from its surroundings, especially if the “background” area is relatively uniform.

48. Spectral resolution
Spectral resolution is referred to as the wavelength range within which a sensor is able to detect and measure radiant energy.
It describes the ability of a sensor to distinguish between wavelength intervals (or bands) in the electromagnetic spectrum.

49. Spectral resolutions of SPOT-5 and Formosat-2 satellites
Spectral resolutions of SPOT-5 and Formosat-2 satellites. (F: Formoat-2, S: SPOT-5)

50. Sensors of higher spectral resolution result in less radiant energy received by detectors, which in turn yield higher signal-to-noise ratios since the noise remains constant.
One way to overcome such disadvantage without reducing the spatial resolution is to choose proper scanning system. For example, a push-broom sensor offers longer dwell time than a whisk-broom sensor, and thus more radiant energy from the target area can be collected and the SNR is lower.

51. Radiometric resolution
Radiometric resolution represents the sensor’s ability to discriminate very slight differences in received radiance. It is defined as the minimum amount of changes in received radiance that can result in a change in detector’s output.
To digitally record the energy received by an individual detector, the continuous range of incoming energy must be quantized, or subdivided into a number of discrete levels that are recorded as integer values.

52. The more levels that can be recorded, the finer is the radiometric resolution of the sensor system (i.e. the more sensitive it is to detecting small differences in energy).
The total number of output levels (grey levels) that can be used by a sensor to record radiant energy is referred to as the dynamic range.

53. Let Lmax and Lmin be respectively the maximum and minimum radiances that can be detected by a sensor. Also, let  be the radiometric resolution of the sensor and NG the dynamic range. The dynamic range and the radiometric resolution of the sensor are related by

54. The dynamic range is governed by the number of bits used by the sensing system to represent the output signal generated by a single detector for a pixel.
For example, an 8-bit image can display a total of 256 (=28) grey levels or digital numbers (DN), i.e. the dynamic range NG = 256.

55. The signal processor of the sensor system converts the radiance received at sensor (Lsensor,) to a corresponding digital number by

56. Temporal resolution
Temporal resolution is the period of elapsed time between images taken of the same object at the same location. For satellite systems temporal resolution is described as the revisit time, which refers to the time it takes for a satellite to return to the same area on subsequent orbits.
The more frequent a sensor is able to return to an exact specific location the greater the temporal resolution. Several observations over time can reveal changes and variations in the object being observed.

57. Generally speaking, it is impossible to simultaneously improve all resolution properties. There are trade-offs between the spatial resolution, spectral resolution, and dynamic range.
For example, a sensor of high spatial resolution has a small IFOV which in turn reduces the amount of radiant energy reaching the sensor. Thus, the dynamic range (or the ability of the sensor to distinguish small difference in radiant energy from ground samples) is also reduced.

58. On the contrary, to increase the amount of energy detected (and thus, the radiometric resolution) without reducing spatial resolution, we would have to broaden the wavelength range of a particular spectral band which would reduce the spectral resolution of the sensor.

59. Illustration of trade-off between spatial and radiometric resolutions
High radiometric resolution, coarse spatial resolution
Fine spatial resolution, low radiometric resolution

61. Linear DN~Radiance Conversion
There exists a linear relationship between the effective radiance received at sensor from a ground sample and the digital number of its corresponding image pixel.

65. In the above equation Rmax is the maximum value of the R() function
In the above equation Rmax is the maximum value of the R() function. Thus, notwithstanding quantization, there exists a linear relationship between the sensor’s output signal, i.e. digital number, and the band effective radiance

66. An example of detailed correction of atmospheric effects
(Forster, Derivation of atmospheric correction procedures for Landsat MSS with particular reference to urban data. International Journal of Remote Sensing, Vol. 5, )
Landsat 2 MSS image,   0.8 – 1.1 m [Band 7].

67. Atmospheric condition at the time of overpass
Temperature 29C
Relative humidity 24%
Atmospheric pressure 1004mb
Visibility 65km
The total normal optical thickness of the atmosphere a = 0.15

68. The transmittances of the atmosphere for a solar zenith angle of 38 and a nadir viewing satellite are
The solar irradiance at the top of the earth atmosphere is E = 256 w/m2.
The total diffusive sky irradiance ED = w/m2.
The path radiance Lu = 0.62 w/(m2-sr).

69. Radiance reaching the sensor
For Landsat 2 MSS data,

70. The reflectance-DN relationship varies with band wavelength interval
The reflectance-DN relationship varies with band wavelength interval. For example, for band 5 of Landsat 2 MSS (  0.6 – 0.7 m [Band 5]) it yields