Radiometric Systems

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Overview
Instrumentation is available to make spatially, spectrally, and temporally resolved radiometric measurements across the spectral region from the vacuum UV through the mid IR (0.2 to 15 microns). Figure 10 divides radiometric instruments into the three basic types: imagers (cameras), spectrometers, and radiometers.


Figure 10. Types of Sensors/Measurements
The trend in demands for measurements with the various instrument types are currently toward higher resolution (spectrally, spatially, and temporally) and greater sensitivity. Radiometrically accurate images derived from radiometric imagers are often the most highly sought data. Instrumentation is typically applied in scenarios such as depicted in Figure 11. Usually, radiometers and spectrometers have FOVs greater than the sources they view and cameras typically have instantaneous FOVs smaller than the sources.


Figure 11. Typical Measurement Scenarios
Each major IR/Vis/UV system typically includes a dedicated data system in the form of a computer which is used for instrument control, data acquisition, and data processing. In the case of radiometers and circular variable filter radiometers, machines based on simple CPUs with general purpose commercially available multiplexing A/Ds are being used. In the case of more sophisticated spectrometers, more sophisticated machines with custom interfaces are being used to both control the instruments and to acquire the data. The most demanding requirements, those of cameras and Fourier Transform Spectrometers, are being met with the most current machines.

Radiometers
The term radiometer is used to describe an optical instrument which collects light and outputs a corresponding signal proportional to the magnitude of the input. The radiometer measures incident in-band radiation as a function of time. It typically includes a simple optical system, often with only a single lens as the collecting and transfer optics, no modulator, and a detector with associated signal conditioning and data handling. The variety of radiometer systems available is extensive. There are chopped and unchopped, analog and photon counting, as well as extremely sensitive and very wide field of view systems. The radiometer is usually the simplest of the radiometric sensors and is the most common system applied. Data processing is generally straightforward for these instruments.

Imaging Radiometers
The terms imager or camera are also used to describe an imaging radiometer. The optical system collects and transfers spatially resolved information to the detector. The typical camera produces a quantifiable in-band radiance distribution map (i.e., a picture). In general the cameras do not use film, rather they produce electrical signals which are interpreted as pictures. The cameras for the UV, Vis, and IR spectral ranges are sufficiently different that they will be described separately.

IR Cameras
The IR cameras in use today include two basic types. The type which was prevalent until recently uses a single detector or linear array of detectors and an optical modulator which mechanically scans the image across the detector in both the x and y dimensions. The second type, which is currently becoming the standard, uses a two dimensional array of detectors known as a focal plane array (FPA). This requires no mechanical scanning and is therefore referred to as a starring array.

The optical train of a representive instrument of the first type contains IR transmitting germanium or silicon elements including two rotating octagonal prisms. These prisms are examples of the optical modulator referred to in Figure 2. The optical train may be examined at several different times to reveal the function of the prisms. The prisms at any particular time appear to the system as merely two windows, having an index of refraction of about 4, inclined with respect to the optical axis. Consequently the prisms serve to effectively shift the optical axis with respect to time and to position different portions of the image on the field stop at different times. By correlating the prism positions and the irradiance within the field stop, an effective wide field of view image can be obtained from this basically single element small field of view instrument. A number of military systems utilize the linear array with mechanical scanning in only one dimension. A linear array, known as the common module, is used in some of these systems.

Infrared cameras based on focal plane arrays are becoming commercially available. Cameras utilizing InSb, Schottky barrier platinum silicide, and bolometric arrays are currently in widespread use. The array is an n by m matrix of detectors usually with some on chip signal conditioning. (The array type cameras should include the pyroelectric vidicon since its function is so similar.)

The IR cameras produce copious quantities of data which must be converted to engineering unit data (EUD). Since they output easily interpreted images, they are the instrument of choice in many measurement programs and are one of the highest demand systems being applied.

In the case of the older, mechanically scanned, single detector cameras, spatial resolution is of the order of 100 by 100 pixels per field, so images are generated requiring only about 20 Kbyte files for storage (for a 10-, 12-, 14-, or 16-bit A/D). The cameras generate twenty five to thirty scans per second, so one second of data requires approximately 0.6 Mbyte of storage. In the case of the FPA, camera data are generated much more rapidly. A 512 by 512 array read 30 times per second generates about 8 Mbytes per second (even when digitized to just 8-bits per pixel).

Low cost data systems are becoming compatible with these data rates and have the computational power required for processing the camera data in reasonable amounts of time. The procedure used to reduce the data is to digitize the analog data produced by the camera, do noise suppression, suppress background contributions, introduce the instrument response, and finally produce engineering unit data in the form of bulk storage records and selected hard copy pseudo color images, isoradiance contours, station radiation, and radiant intensity versus time plots.

Visible and UV Cameras
Cameras operating in the visible and UV portion of the spectrum are typically very similar, with the UV cameras having enhanced operation in the shorter wavelengths. The visible cameras utilize more conventional glasses for their optics and the UV instruments use glasses which transmit well at shorter wavelengths. Radiometrically satisfactory visible camera systems are uncommon. Most video components are directed toward visual appeal rather than radiometric accuracy. Cameras with very high video rates are becoming commercially available.


Figure 12. UV Camera
Image intensifiers are found in the more sophisticated UV systems requiring enhanced sensitivity. An incident photon passes through a window to interact with a photocathode by means of the external photoelectric effect. The photon is converted into a photoelectron which is ejected into the vacuum of the tube and is accelerated to a micro-channel plate (MCP). It strikes the wall of one of the channels where secondary electrons are emitted. This multiplication process is repeated many times as the electrons cascade along the micro-channel under the influence of an electric field. At the exit of the micro-channel as many as a million electrons emerge for every incident photoelectron. Either anodes (single or multiple) or a phosphor screen collect these electrons. The most common UV cameras (shown in Figure 12) utilize a phosphor screen in which the electrons are converted into visible light which is subsequently viewed with a CCD type visible camera. The most common problem with UV cameras is the fact that photocathodes are slightly sensitive to visible light and UV filters are not readily available to adequately reject that unwanted component of radiation.

Spectrometers
The term spectrometer is used synonymously with spectro-radiometer and refers to instruments which measure the spectral distribution of radiation. The more common spectrometer types include: filter spectrometers, dispersive spectrometers, and Fourier Transform spectrometers. The first two types will be briefly described and the FTS will be discussed in some detail.

Filtered Systems
Certain low resolution spectrometers are basically multi element filter radiometers. In these instruments, the optical modulator is some form of optical filter. The most common is the circular variable filter (CVF) radiometer (Figure 13) which incorporates a circular spectrally varying filter rotating in front of a single detector. Its simplicity is its major attraction. Another type utilizes a linearly varying filter placed in front of a linear array. A third type is simply a number of co-aligned filter radiometers packaged as a single unit. Spectral resolution is limited with these devices, but due to their simplicity and dependability their range of applicability is broad.


Figure 13. CVF Spectrometer
Dispersive Systems
The classic spectrometer incorporates a dispersive element such as a prism or grating as part of the optical modulator. Today’s dispersive spectrometer predominately utilizes ruled or holographic gratings. The entire optical modulator consists of a monochromator comprised of an entrance slit, a collimator, the dispersive element, focusing optics, and an exit slit or slits. The current trend is to utilize an array of detectors at the exit plane of the monochromator to simultaneously obtain the entire spectrum of the incident radiation and also serve as exit slits. The dispersive systems utilizing FPA detectors offer many advantages over the older mechanically scanned systems which had single detectors.

FTS Systems
The Fourier Transform spectrometer offers high resolution, broad spectral coverage, high sensitivity, and rapid operation. The most popular type FTS is based upon the Michelson interferometer. Figure 14 shows the optical schematic of this instrument.

Figure 14. Optical Layout of the Fourier Transform Spectrometer
In this example a large reflective element is used to collect radiation which can be limited by the entrance aperture stop. The instrument incorporates a Michelson type interferometer as the optical modulator. Radiation is divided by the beamsplitter to be passed to a fixed and a movable mirror. The path lengths of the light following the two paths are different and when recombined at the detector display interference effects.

Referring to the next figure depicting the Michelson interferometer, the irradiance at the FTS detector is

E = ∫A²(ν)(τρ)²[1+cos{2π(L₃-L₂)ν}]dν
where ν is wavenumbers, A is the magnitude of the incident radiation, L refers to the path lengths shown in Figure 15, τ is the transmission of the beamsplitter, and ρ is the reflectance of the reflective surfaces.


Figure 15. FTS Pathlengths
The resolution of a Fourier Transform Spectrometer varies as the reciprocal of path length difference. Ideally the spectral resolution is

R = 1/ ΔL
Where R is resolution in wavenumbers (cm^-1) and ΔL is pathlength difference in cm.

When the FTS mirror moves and the pathlength difference changes; the difference goes to zero when the two paths are equal. This point is referred to by several descriptive names, such as, Zero path difference point or Grand maximum point. In the following figure this corresponds to the maximum occurring in the 1-2 region (the numbers on the abscissa have no meaning except that the abscissa corresponds to pathlength difference). Since the velocity of the moving mirror is held constant the pathlength difference also corresponds to time. The signal generated by the FTS as the mirror is scanned is known as the interferogram and is a voltage which varies with time. The input radiation consisting of a bundle of different wavelengths produces the grand maximum when the pathlength are equal and all wavelengths constructively interfere and then as the pathlengths differ, destructive and constructive interference effects can be seen.


Figure 16. Signal Interferogram
As the mirror scans, a laser (monochromatic souce) is also input through the FTS and this source generates, on a separate detector, a reference signal referred to as the laser interferogram. It is a simple sinusoidal signal.


Figure 17. Laser Interferogram
This signal is used to generate pulses, at some multiple of zero crossings and peak values, which are used to control sampling of the signal interferogram. The laser commonly used for IR FTS instruments is the HeNe producing a laser line at 0.632995 microns. The zero crossing of the laser interferogram are therefore spaced apart at 0.3165 microns. This spacing determines the lowest wavelength light that can be unambiguously determined from the interferogram. Using Nyquist criteria the shortest wavelength which can be determined must be at least twice the sampling interval.

λ_min > 2 x sample interval
The following tables include some useful FTS relationships and introduce at least one new term. The pathlength difference is referred to as the retardation.

Retardation (cm)	Resolution (cm-1)	Number of Points	Binary Representation
0.125	8	1975	2K
0.250	4	3949	4K
1	1	15798	16K
2	0.5	31596	32K
10	0.1	157979	160K
100	0.01	1,579,791	1.6M
valid for one sample per laser period (every other laser zero crossing)

Velocity (cm/sec)		Samples/second
Mechanical	Optical	@ 1 per period
0.05	0.1	1580
0.5	1	16K
2.5	5	80K
5	10	160K

Samples/Laser Period (0.6328 μ)	Min λ (μ)	Max ν (cm-1)
2	0.6328	15802
1	1.2656	7901
½	2.5312	3950

The FTS mirror usually moves at a constant velocity resulting in the ability to relate a frequency to the laser interferogram. This may be either the frequency at which samples are generated by the FTS or the frequency of the laser interferogram (the situation for one sample per laser period). The frequency of the radiation which is be measured by the FTS detector is related to the time domain signal with the formula

Modulated Frequency = 2 (Velocity of Mirror) (Band in cm^-1)
[e.g., 50000 Hz = 2 (5 cm/sec)(5000 cm^-1) and 20000 Hz = 2 (5 cm/sec)(2000 cm^-1) where these examples correspond to the frequencies of 2 and 5 micron wavelength radiation]

Note: To convert wavenumbers to wavelengths divide 10000 by the known number; i.e., ν (in cm^-1) = 10,000 / λ (in microns) or λ (in microns) = 10,000 / ν (in cm^-1)

The time domain interferogram is converted to a spectral domain signal by mathematically performing the Fourier Transform on the data. In the non-ideal case several additional steps are required. The data reduction procedure consists, first, of digitizing the signal produced by the spectrometer at discrete spatial steps, using the sample pulses generated by the laser interferogram. Then, finding the Grand Maximum position in the data file, to use as a reference point. If many interferograms are being examined, the files may need to be aligned so that the Grand Maximum occurs at the same position in each file. Then, since the interferogram may include a DC offset, it must be removed. The interferograms may be averaged to improve signal to noise. At this point a step is required for correcting the data to eliminate effects due to truncation of the data introduced by finite sampling; this mathematical step will not be described herein, but is referred to as apodization. At this point the time domain data undergoes Fourier transformation to be converted to the spectral domain. Then standard steps such as applying the instrument response and suppressing background contributions are performed to generate engineering unit data in the form of spectral radiances or radiant intensities.

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