FLIR Concept

1. FLIR Concept Prepared by Ernest Grimberg - Opgal chief scientist

2. General background. Physical Constants. Basic radiometric concepts. Black body radiation. Optics - introduction. IR Detectors. Spatial resolution and thermal resolution. Signal processing block diagram. Table of contain

3. General Background electromagnetic waves

4. General Background electromagnetic waves Plane polarized EM wave Speed of an EM wave Link to a more detailed paper

5. General Background electromagnetic waves • ENERGY TRANSPORTED BY AN EM WAVE • The B and E fields of an electromagnetic wave contain energy. e.g Heat from a light bulb • The rate of energy flow per unit frontal area (Energy flux) , • (watts/m2) • In general, the energy flux or POYNTING VECTOR . • Notice how the vector product gives the travel direction of an EM wave.

6. General Background electromagnetic waves INTENSITY OF AN EM WAVE Consider a point in space. Take x = 0 for convenience. Hence the average energy flux Wave Intensity I =

7. General Background electromagnetic waves

8. General Background electromagnetic waves propagation

9. Physical Constants

10. Angle definitions Planar angle =(arc length)/radius [radians] Solid angle = (surface area)/radius [steradians]

11. Angle approximations formulas =², ( in rad), for <0.4 rad (23°), Max. Error 1.5% =sin ²()( in rad), for <0.4 rad (23°), Max. Error 1.5%

12. Radiometric quantities and formulas

13. Blackbody Radiation The spectral radiant emittance formula is: T is the absolute temperature in degrees Kelvin. Spectral radiance L() is equal to M()/ because blackbodies are Lambertian sources:

14. Blackbody Radiation

15. Blackbody Radiation

16. Blackbody Radiation

17. Optics, F/number F/number (f#) or “speed” of a lens is a measure of the angular acceptance of the lens. f represents the focal length d represents the entrance pupil diameter of the lens For small  angles the numerical aperture is approximately equal to 0.5F#.

18. Optics, F/number When an optical lens is used to image a scene, of radiance equal Lsc, on a detector faceplate or on film the faceplate radiance may be obtain from the following formula: Lfp represents detector faceplate radiance in W/(m*m*steradian) Lsc represents scenery radiance in W/(m*m*steradian) Tr represents the lens transmittance m represents the magnification from scene to detector faceplate

19. Optics, Diffraction limit Diffraction, poses a fundamental limitation on any optical system. Diffraction is always present, although its effects may be masked if the system has significant aberrations. When an optical system is essentially free from aberrations, its performance is limited solely by diffraction, and it is referred to as diffraction limited. In calculating diffraction, we simply need to know the focal length(s) and aperture diameter(s); we do not consider other lens-related factors such as shape or index of refraction. Since diffraction increases with increasing f-number, and aberrations decrease with increasing f-number, determining optimum system performance often involves finding a point where the combination of these factors has a minimum effect.

20. Optics, Diffraction limit continue Fraunhofer diffraction at a circular aperture dictates the fundamental limits of performance for circular lenses. It is important to remember that the spot size, caused by diffraction, of a circular lens is where d is the diameter of the focused spot produced from plane-wave illumination and  is the wavelength of light being focused. The diffraction pattern resulting from a uniformly illuminated circular aperture is shown in the image below. It consists of a central bright region, known as the Airy disc, surrounded by a number of much fainter rings.

21. Optics, Diffraction limit continue Each ring is separated by a circle of zero intensity. The irradiance distribution in this pattern can be described by where I0 = peak irradiance in the image. J1(x) is a Bessel function of the first kind of order unity, and where  is the wavelength, D is the aperture diameter, and  is the angular radius from pattern maximum.

22. Optics, Diffraction limit continue Energy Distribution in the Diffraction Pattern of a Circular Aperture Ring or Band Position (x) Relative Intensity (Ix/I0) Energy in Ring (%) Central Maximum 0.0 1.0 83.8 First Dark 1.22 0.0 First Bright 1.64 0.0175 7.2 Second Dark 2.23 0.0 Second Bright 2.68 0.0042 2.8 Third Dark 3.24 0.0 Third Bright 3.70 0.0016 1.5 Fourth Dark 4.24 0.0 Fourth Bright 4.71 0.0008 1.0 Fifth Dark 5.24 0.0

23. Optics, Diffraction limit continue The graph below shows the form of both circular and slit aperture diffraction patterns when plotted on the same normalized scale. Aperture diameter is equal to slit width so that patterns between x values and angular deviations in the far field are the same.

24. Optics, Diffraction limit continue The graph below shows the diameter of the first circular bright disc versus optics f# for two different wavelengths: 4 microns and 10 microns respectively.

25. Optics Detector relations Assuming that the detector is a two dimensional matrix of n_x by n_y elements, and that each detector element size is d_x by d_y meters, and that the optics focal length is f meters, the instantaneous field of view (IFOV), on X and Y directions, are given by the following relations:

26. Optics Detector relations continue Assuming that the detector is a two dimensional matrix of n_x by n_y elements, and that each detector element size is d_x by d_y meters, and that the optics focal length is f meters, the field of view, on X and Y directions, are given by the following relations:

27. Detection, Orientation, Recognition, and Identification Task Line Resolution per Target Minimum Dimension Detection 1.0 ± 0.25 line pairs Orientation 1.4 ± 0.35 line pairs Recognition 4.0 ± 0.8 line pairs Identification 6.4 ± 1.5 line pairs

28. IR Detectors Quantum noise limit The quantum noise difference in temperature (QNETD) for cooled detectors is limited by the signal quantum noise. n represents the amount of photoelectrons collected from the scenery.

29. IR Detectors Quantum noise limit continue The quantum noise difference in temperature (QNETD) for cooled detectors is limited by the signal quantum noise.

30. IR Detectors Quantum noise limit continue The quantum noise difference in temperature (QNETD) for cooled detectors is limited by the signal quantum noise.

31. IR Detectors technology There are two verydistinctive detector technologies: the direct detection (or photon counting ), and thermal detection. Direct detection technology (photon counting) translates the photons directly into electrons. The charge accumulated, the current flow, or the change in conductivity is proportional to the scenery view radiance. This category contains many detectors, like: PbSe, HgCdTe, InSb, PtSi etc. Except for FLIRs working in the SWIR range, all the FLIRs based on the direct detection technology are cooling the detectors to low temperatures, close to –200 degrees Celsius.

32. IR Detectors technology Thermal detection technology. These detectors are using secondary effects, like the relation between conductivity, capacitance, expansion and detector temperature. The following detectors are classified in this category: Bolometers, Thermocouples, Thermopiles, Pyroelectrics etc. Usually these detectors do not require cryogenic temperatures.

33. IR Detectors description • Any IR “detector” (except for the near IR spectra) is an assembly that contains: • A Focal Plane Array (FPA), • A dewar or a vacuum package, • A cooler or a temperature stabilization device, • and in most of the cases a cold shield or a radiation shield.

34. IR Detectors description continue

35. IR Detectors, DEWARS Description

36. IR Detectors, InSb spectral band description 320256 InSb FOCAL PLANE ARRAY DETECTOR

37. Microbolometer detector basic concept The original design disclosed by Honeywell.

38. Microbolometer detector basic concept The original design disclosed by Honeywell.

39. Microbolometer detector basic concept Real picture. Sofradir’s detector.

40. Spatial resolution and thermal resolution.

41. Spatial resolution and thermal resolution. The spatial resolution and the thermal resolution will be analyzed Assuming that the thermal cameras can be described by linear models.

42. Spatial resolution and thermal resolution continue Thermal camera response to any input signal is given by : Trepresents camera’s transfer function. Recoll: T depends on x,y only, therefore assuming linearity :

43. Spatial resolution and thermal resolution continue Therefore the thermal camera response to any input signal is given by : hrepresents camera’s impulse response function. The camera impulse response is given by convolving its subsystems. represents the convolution operator.

44. Spatial resolution and thermal resolution continue • Example. Estimate the MTF of a FLIR camera based on a the uncooled • microbolometer detector manufactured by Sofradir. • The input data for performance estimation is: • 1. Optics focal length = 0.1 m, • 2. Optics f number = 1.17 , • 3. Optics transfer function at 1.1 cycles/milliradian = 0.75 • Gimbals line of site stabilization standard deviation equals 100 microradian.

45. Spatial resolution and thermal resolution continue Assuming diffraction limit optics performances : But according to the input data: Optics transfer function at 1.1 cycles/milliradian = 0.75

46. Spatial resolution and thermal resolution continue Assuming geometrically limited optics :

47. Spatial resolution and thermal resolution continue Assuming that the detector impulse response is geometrically limited:

48. Spatial resolution and thermal resolution continue Stabilization impulse response for a standard deviation of 100 µrad :

49. Spatial resolution and thermal resolution continue The electronics is model as a low pass filter on horizontal direction therefore :

50. Spatial resolution and thermal resolution continue Entire system impulse response is estimated by the following process :