Frequently Asked Questions
 What is meant by "absolute temperature" and "differential temperature"?
 What is "radiometric temperature difference"?
 How are target feature sizes calculated?
 What blackbody specs are important for measuring Minimum Resolvable Temperature Difference (MRTD)?
 Can a thermometer with .01ºC accuracy be used to calibrate a blackbody to its full spec of .025ºC?
 What is an appropriate set of 4bar targets for MRTD (Minimum Resolvable Temperature Difference) measurement?
 Is an edge target or a slit target more appropriate for MTF (Modulation Transfer Function) measurement?
What is meant by "absolute temperature" and "differential temperature"?
Some SBIR blackbody controllers allow control of either absolute or differential temperature. Absolute temperature is the temperature of the blackbody surface. Differential temperature is the difference between the blackbody surface temperature and the temperature of some other surface.
For example, if you were controlling the absolute temperature of the blackbody and the setpoint was +20.000°C, then the temperature of the blackbody surface would be controlled at +20.000°C. If you were controlling the differential temperature of the blackbody, the blackbody surface would be held +20.000°C higher than the temperature of the blackbody’s reference temperature probe. As the temperature of the reference probe moved higher or lower, the temperature of the blackbody would move higher or lower to maintain the proper temperature difference.
Normally, the reference probe is mounted in a target in front of the blackbody surface. This allows control of a precise temperature difference between the blackbody and the target, creating a temperature contrast to be viewed by the unit under test.
SBIR instruments label the blackbody temperature as "T2", and the reference probe temperature (target temperature) as "T1". So when the instrument is in absolute control mode, it is controlling T2. When it is in differential control mode, it is controlling dT = T2 – T1.
What is "radiometric temperature difference"?
Other names for this quantity are "effective differential temperature", "radiometric delta T", "RDT", or "RdT".
To achieve a given RDT, a blackbody must produce a difference in radiance between the target and the IR source which is numerically equal to the difference in radiance, integrated over the spectral band of interest, that would be produced by an ideal target at 298K and an ideal IR source maintained at an "effective" commanded temperature differential above or below 298K.
For more detail on this subject, see the application note Radiometric Temperature: Problems and Solutions.
How are target feature sizes calculated?
Generally, target feature sizes are straightforward trigonometric calculations. For repeated patterns such as 4bar targets, make sure that you distinguish between "bar width" and "cycle width", a cycle being a bar and the adjacent space. Apart from that distinction, the calculation of feature sizes uses the same formula for any shape: bars, squares, round apertures, etc.
To calculate the width of a target feature:
feature size in inches = .001 x collimator focal length in inches x feature size in milliradians
or
feature size in inches = .0005 x collimator focal length in inches / cycles per milliradian
The above formulas are approximations, and work well for feature sizes less than 100 milliradians.
The bars in a 4bar pattern typically have a 7:1 aspect ratio with equal bar and space widths, so the resulting pattern (4 bars and 3 spaces) is square.
What blackbody specs are important for measuring Minimum Resolvable Temperature Difference?
Surprisingly, Minimum Resolvable Temperature Difference (MRTD) measurements can be made with an accuracy better than the "total system uncertainty" spec of the blackbody. For small incremental temperature measurements made near zero DT and spaced closely in time, measurement accuracy is determined by the temperature noise (short term stability) and linearity of the blackbody, rather than its absolute accuracy.
Recall that MRTD measurements are made by recording the minimum resolvable positive contrast, the minimum resolvable negative contrast, and then averaging the two. This removes any inaccuracies in the reference (target) temperature. Additionally, the MRTD measurement now depends not on the accuracy of the blackbody, but on its linearity (that is, any offset error in the blackbody temperature will eliminated the positive and negative temperatures are averaged. The only remaining error is linearity: how well the slope of the temperature calibration curve matches true temperature).
Temperature measurement linearity for an SBIR 2000 Series Blackbody is better than .0015°C/°C at any point within the blackbody's range. Linearity is even better near zero DT: on the order of .0010°C/°C. So for small MRTDs (half a degree or less), error due to blackbody nonlinearity is less than the resolution of the temperature readout. The only significant error source is the short term stability of the blackbody system. The data sheet for the 2000 Series Blackbodies specifies short term stability as ±.003°C. This is a conservative spec  the blackbodies easily exceed this level of performance, particularly near zero DT in a stable lab environment. You should be able to make your MRTD measurements with blackbody uncertainty of better than ±3mK.
Can a thermometer with .01°C accuracy be used to calibrate a blackbody to its full spec of .025°C?
Normally, you want a 4:1 ratio between the accuracy of the calibration equipment and the accuracy of the equipment being calibrated. But acceptable calibration can be achieved even if this guideline cannot be met.
The 4:1 ratio comes from MILSTD45662A, paragraph 5.2, which specifies that the uncertainty of measurement standards should not exceed 25% of the acceptable tolerance for a characteristic being calibrated. However, MILSTD45662A allows deviation from this ratio provided the adequacy of the calibration is not degraded.
SBIR's differential blackbody sources are specified with a total system uncertainty of .025°C for temperatures near 25°C and near zero DT. Calibration is performed using a thermometer with accuracy of .01°C, so a 2.5:1 ratio exists between the measurement standard and the characteristic being calibrated.
The limiting factor in calibration of differential blackbodies is the unavailability of a better thermometer. An SPRT and resistance bridge, such as the Rosemount 162CE and ASL F17 used in SBIR's primary standards lab, provide greater accuracy but cannot be used because of physical limitations on the probe: the SPRT diameter is too large and its immersion depth requirement is too great to allow use in a blackbody calibration. The SBIR Model 104 thermometer is the most accurate thermometer available with temperature probes of suitable form factor for blackbody calibration.
MILHDBK52A, paragraph 5.2(c) permits ratios as close as 1:1 when stateoftheart limitations preclude a higher accuracy ratio. The 2.5:1 ratio provided by the SBIR Model 104 thermometer is well above that minimum. In addition, the Calibration Data Sheets (QF214009) that are recorded during recalibration of both the Model 104 thermometer and the differential blackbodies consistently show a level of error that is comfortably below the accuracy specification of the instruments. Also, crosschecking of blackbody calibration using a different Model 104 thermometer has shown correlation on the order of .01°C, demonstrating that the adequacy of the blackbody calibration has not been compromised.
What is an appropriate set of 4bar targets for MRTD (Minimum Resolvable Temperature Difference) measurement?
There are two references for selecting a set of 4 bar targets with the spatial frequencies covering a customer’s range of interest.
The TriServices Working Group recommends 4 spatial frequencies in their Guide for Preparing Specifications for Thermal Imaging Sets. These are recommended frequencies, not requirements. They are:
0.2 f_{o} 0.5 f_{o} 1.0 f_{o} 1.2 f_{o}
f_{o} is 1/(2 IFOV) where IFOV is the Instantaneous Field of View, (also called the DAS, Detector Angular Subtence).
Holst simply refers to measuring MRTD in 3 places. A high frequency measurement (the value is not specified), a mid frequency test (the fo value described above), and a low frequency measurement which he has dependent on viewing distance.
Since fo is the theoretical Nyquist frequency limit if a starring array has a 100% fill factor, the 1.0f_{o} and 1.2f_{o} values are adequate for the high frequency limit. The 1.2f_{o} value is somewhat arbitrary, so a range of 1.2f_{o} to 1.5f_{o} should be acceptable (and is actually discussed in the Tri Services Guide).
The low frequency measurements establish a limiting asymptote, so having both frequencies is useful. The values don’t have to be exactly 0.2f_{o} and 0.5f_{o}. If the number of targets available for testing is limited, then a single value somewhere between 0.2f_{o} and 0.3f_{o} should be used.
Summary:

Where:
f_{o} = 1/(2*IFOV)
IFOV = (Detector Element Size)/(Focal Length)
Is an edge target or a slit target more appropriate for MTF (Modulation Transfer Function) measurement?
SBIR has chosen the edge target for use in its IRWindows standard target set. The signal from scanning across the edge target is differentiated to get the line spread function which would have been provided by a slit target. A Fourier Transform is then performed on this line spread function to generate the MTF.
There are several advantages to the edge target over the slit target. The first is its general applicability. A slit target must be matched to the element size of the IR sensor to provide an accurate spread function. The slit width should be no more that 0.1 IFOV, with a narrower width even better. The target must be carefully manufactured to insure constant width over the height of the slit. A slit this small severely limits the flux passing through it, decreasing the signaltonoise ratio. A separate target must be manufactured for each element size of interest.
The edge target avoids all of these problems. A single edge can be used for any size element, and the manufacturing constraints are not so severe. The signal can be increased independent of the target size, insuring the maximum signal noise ratio. The only drawback of the edge target is that the differentiation step increases the noise sensitivity of the MTF measurement, which is dealt with independently using other methods.
For the IRWindows system, the advantages of the edge target over the slit target far outweigh the disadvantages.