Measuring the modulation transfer function of a type II superlattice focal plane array
In the field of remote sensing, successful high-resolution imaging requires a detector that responds accurately to incoming visual data, especially at the high spatial frequencies arising from closely spaced visual elements. One useful performance metric is the detector's modulation transfer function (MTF), which specifies the ratio of contrast modulation between image space and object space as a function of spatial frequency. Informally, a higher MTF corresponds to better resolution of fine details. Accurate MTF characterization can assist system designers in selecting the appropriate detector for a given application.1
While no practical detector array is perfect, new detector technologies based on type II superlattices show good potential to match the performance of conventional mercury cadmium telluride (HgCdTe) detectors, without the need for extensive cooling systems.2 A type II superlattice typically contains alternating thin layers of indium arsenide (InAs) and gallium antimonide (GaSb), or other III-V binary materials (i.e., consisting of elements from groups III and V of the periodic table). Such a device can be band-gap engineered to respond strongly at the infrared wavelengths where atmospheric transmissions are maximized.
We have demonstrated a new type of device called a complementary barrier infrared detector (CBIRD)3 and have also developed a large-format array (1024 × 1024 pixels) using this technology.4 The individual pixel values are accessed via a readout integrated circuit (ROIC), a gridlike device mated to the array. FLIR Systems (formerly Indigo Systems) has recently introduced an ROIC that is optimized to operate with type II superlattice detectors.5
Generally, the optics in a remote sensing system direct an image of the scene onto a grid of light-sensitive pixels called a focal plane array (FPA). Due to the diffraction of light, every point source of light in object space gives rise to a circular pattern. As shown in the inset of Figure 1, the center portion of the pattern, known as an Airy disk, may span multiple pixels, with a width given by the diffraction limit: 2.44λf, where λ is the wavelength and f is the f-number of the lens. One way to increase detector precision in this case without increasing pixel density is by reducing the active (optical) area of each pixel. The ratio of active area to total area is known as the fill factor and is normally expressed as a percentage. In the inset, the larger squares of the lattice have dimension a×a, corresponding to a fill factor of 100%, while the squares with dimension b×b correspond to a somewhat smaller fill factor. Fill factors less than unity have a lower signal to noise ratio, since photons are lost in the gap between pixels. On the other hand, because each pixel is completely delineated down to the bottom contact, lowering the fill factor reduces lateral carrier diffusion considerably (with the exception of shorter wavelengths, which are absorbed near the top surface and can diffuse into neighboring pixels via the very thin layer of heavily doped common electrical contact).
A detector's resolution is limited by its Nyquist spatial frequency (nominally the reciprocal of twice the pixel pitch). At that frequency, alternating crests and troughs of intensity fall on successive pixels. For example, the Nyquist spatial frequency along one dimension of a 30μm pixel array is (2μm × 30μm)−1=16:67 cycles/mm. However, in the presence of a weak signal, with fewer photons striking each pixel, somewhat higher spatial frequencies can be sampled if the fill factor is less than unity. For this reason, it is useful to decompose an FPA's MTF into the product of a geometric MTF and a detector MTF.6 The detector MTF is related to the device's electro-optical properties—diffusion length, thickness, absorption coefficient, and junction size—and is generally maximized by having a large fill factor, a thin detector and short diffusion length, a large quantum efficiency, and a large absorption coefficient. The geometric MTF is expressed as a sinc function: sin(πbf )/(πbf ), where b is the active pixel size and f is the spatial frequency, both measured along the dimension of interest. At the Nyquist spatial frequency, this function has a maximum value of 0.64. The CBIRD detector, with its 27 × 27μm pixels on a 30 × 30μm grid, has a higher effective Nyquist frequency (∼18.5 cycles/mm) and a greater geometric MTF than it would if its pixels were a full 30 × 30μm.
We set up an optical system with a 320 × 256 pixel CBIRD FPA having a 30μm pixel pitch (matching the dimensions of the FLIR Systems ROIC). Each pixel's active area was a square 27μm on a side, yielding a fill factor of (27μm/30μm)2, or 81%. We next measured the overall MTF of the system, in both the horizontal and vertical orientations, by taking the derivative of an oversampled tilted knife-edge image and computing the absolute value of the Fourier transform of the resulting line spread function.7 An infrared camera system's MTF represents the product of the MTFs of its many components: optics, detector, preamplifier, analog-to-digital converter, and image processing system.8 However, having made the assumption that the contributions of the first two will dominate all others, we estimated the detector's MTF in each direction by factoring out the MTF of the lens from that of the entire system.
As is immediately evident from the graph in Figure 1, the computed MTFs of our detector fall below the geometric MTF of a detector with 27μm pixels, as well as one with 30μm pixels. Especially near the Nyquist frequency, the system behaves as if the detector's pixels were considerably larger than they actually are. Approximating all curves as Gaussians, the line fit that most closely matches both measured MTFs is that of a hypothetical detector with a pixel pitch of 36μm. We conclude that other mechanisms that degrade MTF may be active, especially at higher frequencies, and we are now actively investigating the possible origins of this effect.
The authors are grateful to Meimei Tidrow and Sumith Bandara of the US Army's Night Vision and Electronic Sensors Directorate for their encouragement and support during the development of III-V FPAs. We also acknowledge support from Lucy Zheng of the Institute for Defense Analyses, technical support from Susan Petronio and Eric Kurt of FLIR Systems, and technical support from Mark Stegall of SE-IR Corporation. The research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the NASA. Government sponsorship acknowledged.
Sir (Don) B. Rafol received his MA in physics from Kent State University (1984) and his PhD in physics from the University of Illinois at Chicago (1991). His research interests include the origin of FPA noise, detector dark current and noise, transport properties, MTFs, and detector/amplifier composites.
