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Dynamic radiometric calibration andradiometric matching of multiple
microbolometer detector arrays

Hagen, Nathan

Nathan Hagen, "Dynamic radiometric calibration and radiometric matching ofmultiple microbolometer detector arrays," Proc. SPIE 11502, Infrared Remote
Sensing and Instrumentation XXVIII, 115020M (20 August 2020); doi:
10.1117/12.2567811
Event: SPIE Optical Engineering + Applications, 2020, Online Only
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Invited Paper

Dynamic radiometric calibration and radiometric matching of multiple
microbolometer detector arrays
Nathan Hagen
Utsunomiya University, Department of Optical Engineering, Center for Optical Research andEngineering (CORE), Utsunomiya, Tochigi 321-8585 Japan
ABSTRACT
While uncooled microbolometer cameras have made infrared imaging accessible to a much wider range of applications
than their cryo-cooled competitors, they are notorious for having poor noise performance and problems with calibration
drift. The drift causes microbolometer cameras to lose radiometric accuracy over time, and this is a serious problem
for radiometrically combining multiple detector arrays because the drift is not the same for each camera, and existing
calibration methods cannot adequately compensate for it. We show methods to dynamically correct for calibration drift
during measurements, so that multiple detector arrays can be kept in radiometric agreement with one another.
Keywords: infrared imaging, calibration, drift, microbolometer, radiometry

1. INTRODUCTION
Uncooled microbolometer detector arrays are a convenient and low-cost approach to thermal imaging, but are notorious forhaving high noise, sensitivities that vary from pixel to pixel, and for calibration drift. In order to calibrate the pixel-dependent
sensitivities, the traditional approach is to block the camera’s field of view with a uniform-temperature shutter (temperature
Tcool ) followed by a second uniform-temperature shutter (temperature Twarm ). With these two reference images, we caneasily caclulate the appropriate offset and gain values at each pixel (as in Sec. 2 below). However, as soon as the calibrationis complete, and the shutters open to reveal the scene to the sensor, the calibration parameters immediately start to change,as the detector array, camera housing, and lens change in temperature. While the changes are gradual, a recalibration every
couple of minutes is generally needed in order to compensate for the drift in the calibration paremeters.
A number of researchers have tried to improve on this situation. Parrish and Woolaway modified the calibration
procedure to create a different set of calibration parameters for a range of detector array temperatures.1 By using atemperature sensor placed on the FPA itself, we can select the appropriate calibration set to fit the current state. Indeed,something like this is basically implemented on all commercial microbolometer cameras today, though the correction istypically only applied to the gain parameters. A similar approach, refined to provide more fine-grained correction has been
implemented by Nugent et al. and Liang et al.2, 3 Other researchers have tried alternative system architectures, such as
replacing the opaque shutter with a partially-transparent, partially-reflecting shutter,4 or with a spherical mirror having acentral hole.5
While these methods have interesting new properties, and some improve the current state of affairs, my own experiencehas been that these methods still have trouble maintaining absolute radiometric accuracy to much better than about 1 ◦C.
That is, if we use two microbolometer cameras, corrected with the above methods, viewing the same scene, the cameras
can achieve consistent agreement about the scene radiance temperatures to within about 1 ◦C. One also finds that, despite
the attempts at drift correction, the correction is not quite consistent. Even if the cameras are forced to match one anotherduring an initial calibration, they will immediately start to drift apart during operation, on the scale of tens of millidegrees
in just a few seconds. In fact, this problem of achieving accurate radiometric matching of microbolometer cameras has
been considered to be so intractable that a number of experts have given it up as hopeless.
In the discussion below, we show that, while tricky, it is not at all a hopeless problem, and we show how to modify
an array of microbolometer cameras such that radiometric matching can be achieved. We start by reviewing the “static
calibration” achieved using a pair of shutters. If the bulk of the error can be considered as a scalar offset across the entire
array (that is, we need not consider pixel-to-pixel variations, for short term periods) then we can achieve the same effectby placing two reference blackbodies into the scene itself. Any change in the reference blackbodies within the scene canbe approximated as global changes to the entire FPA, such that forcing the cameras to agree on the radiance temperatures
Infrared Remote Sensing and Instrumentation XXVIII, edited by Marija Strojnik,
Proceedings of SPIE Vol. 11502, 115020M · © 2020 SPIE
CCC code: 0277-786X/20/$21 · doi: 10.1117/12.2567811
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of the blackbodies effectively brings them into radiometric matching. Inserting reference blackbodies into every scene
to be measured is impractical, but if we block a portion of each camera’s field of view, we can place a reference source
into the blocked region, and this can be maintained quite close to the camera. With multiple cameras all viewing thesame reference sources, it becomes possible to maintain radiometric matching of multiple detector arrays to within about
4×NETD despite the problems of detector drift, for several minutes. After several minutes, pixel-dependent variations start
to become intolerably large, so that renewed static calibrations, or corrections such as those discussed in Refs 2, 3 become
necessary to maintain radiometric matching.

2. STATIC CALIBRATION OF MICROBOLOMETER CAMERA IMAGES
The measurement g, in units of digital counts, at a given pixel can be approximated by6∫
g = α + γ0 Apix ΩR(λ) τ(λ) Lobj (λ) dλ ,(1)where L(λ) is the object radiance spectrum, Apix is the pixel area, Ω is the solid angle of the lens exit pupil as viewed by the
pixel, R is the detector responsivity, and τ is the optical transmission. The “offset” and “gain” parameters of the camera arerepresented by α and γ0 . The detector element also receives light from the surrounding background (such as the camera
housing), but this can be subsumed into an offset term that varies with camera temperature, α(Tcam ). The responsivity andthe optical transmission also have some temperature dependence, which we can represent as γ0 (Tcam,Tfpa ). Here Tcam is theaveraged temperature of the camera housing, and Tfpa is the temperature of the focal plane array itself.
Taking the radiance-spectrum weighted averages of the responsivity and optical transmission, (1) becomesg = α + γ0 Apix Ω ∆λ R̄τ̄ L̄ = α + γ1 L̄ ,(2)

where overbars indicate an average, and the various object-independent parameters have been subsumed inside the newgain parameter γ1 . If the scene object temperatures do not occupy a wide range, then we can approximate the radianceas a linear function of temperature, and the radiance-based measurement equation of (2) can be approximated with atemperature-based one:g ≈ α + γTobj .
(3)
Although the radiance-based method is more accurate, we will use the temperature-based equation below in order to keep
the discussion as simple as possible.
The offset and gain are unknown parameters that must be calibrated. In order to determine their values, we can place two
blackbody objects of different temperatures in front of the camera, and measure the response to each, and solve for α and γ.
If we designate the cooler object temperature as Tcool and the warmer object temperature as Twarm , then the measurements
at each pixel can be written asgcool = α + γ Tcool − Tcool ,gwarm = α + γ Twarm − Tcool .
From these, we see that the offset value is simply α = gcool (the measured pixel value in counts when viewing the coolreference), and the gain value γ in counts/◦C asγ=

gcool − gwarm.
Tcool − Twarm(4)

Thus, if a pixel measures gcool = 7000 and gwarm = 5000 for objects at temperatures Tcool = 20 ◦C and Twarm = 30 ◦C, thenthe estimated offset and gain values will be α = 5000 cts and γ = 200 cts/◦C.
We convert the raw pixel value g for any scene (in units of counts) to estimated radiance temperature T̂ withT̂ =1(g − α) + Tcool .
γ(5)This is the conventional “nonuniformity correction” (NUC). Since the α and γ parameters do not change from one calibration
to the next, we will refer to them together as the “static calibration”.

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3. DYNAMIC CALIBRATION
After the static calibration is complete, we raise the camera shutter and expose the detector array to the scene. First
we consider placing two blackbodies into the scene, where Tcool and Twarm are their temperatures as estimated by thecamera, while Wcool and Wwarm are the a priori known blackbody temperatures. In practice, we can use thermisters on
the blackbodies to tell us W. For radiometric matching of cameras, we can alternatively use one cameras as a “reference”
camera, and force all of the other cameras viewing the blackbody references to match to it. This latter method maintains
matching between cameras but sacrifices absolute radiometry.
The largest part of the calibration drift is the same for all pixels, and so we can use the pixels that view the reference
blackbodies to correct the pixels viewing the remainder of the scene. Thus, the dynamic calibration gives a corrected
temperature T 0 from the initial temperature T estimated at each pixel in a camera using
T 0(x, y) = ω + β T(x, y) ,
where

(6)

ω = Wcool − βTcool

is the dynamic offset correction factor, andβ=

Wwarm − Wcool
Twarm − Tcool

is the dynamic gain correction factor. These are “dynamic” because they are estimated and applied to correct eachmeasurement frame. As a check, we can substitute Tcool for T in (6) and verify that we get the result T 0 = Wcool . Likewise,
substituting Twarm into T gives T 0 = Wwarm , as we expect. In addition, if we have only one reference blackbody in the scenerather than two, then we can apply an offset-only dynamic correction by setting β = 1.
While applying the dynamic correction (6) is straightforward and the procedure is simple enough to apply to a video
stream coming from a high-resolution camera, placing reference blackbodies into each scene is impractical. We need ameans of putting the reference sources into the camera’s field of view while keeping them close to the camera body itself.
To do this, we can construct an aperture that obstructs the cameras’ field of view, as in Fig. 1. If we ignore for the moment
the fact that these reference sources will be out of focus, then we can place an array of blackbody sources around the edgeof the aperture, and these will be visible at the edges of the cameras’ fields of view. Using film-based heater elements
and thermisters, we can coat the emitting surface of these reference sources to give high emissivity, and control theirtemperatures to give inputs for Wcool and Wwarm .
While each of the reference sources of Fig. 1 can be independently controlled, it is difficult to get all of the various
thermisters to agree with one another. Since each camera will generally see not only its own pair of reference sources but
also one of the adjacent camera’s reference sources, this overlap can be use to improve agreement among the cameras.
However, radiometric matching of the cameras is still not ideal.
In order to improve the matching of cameras, we would like all of the cameras to be looking at the same reference
blackbody sources. In order to make this possible, we can replace the array of reference sources placed along the external
aperture with an array of imaging mirrors, designed to relay the image of the two reference sources into each camera’s
respective field of view. The resulting layout is shown in Fig. 2. A convenient location for placing the reference sources isin the interstitial space between the cameras, so that the re-imaging mirrors need not have a severe tilt angle.

4. VIEW OBSTRUCTION AND BLURRING
Because we are placing the reference sources at a short dictance in front of the camera lens, their image will be blurry at
the detector array. This by itself is not a problem, since there is no need to spatially resolve the references — we need only
average the temperature that we measure across the face of the blackbody. However, the blurring means that we need toallow enough margin so that the temperature profile of the scene does not blur into the image of the reference source. In
the case of Fig. 2, where the mirrors are imaging the sources onto the detector arrays, the images of the blackbodies will bein focus, but the mirrors themselves will be out of focus. As a result, the margin that we need to allow is the same for bothcases (Fig. 1 and Fig. 2).

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M 3A

M 0B
M3A M3B M4A M4B M5A M5B

3

4

5

0

1

2

camerablock
detectorarray 0detectorarray 3M0B M0A M1A M1B M2A M2BcamerasA
B

referencesources

M 0A M 0B(a)

M 3A M 3B(b)Figure 1: An example layout for a 2 × 3 array of cameras, using an array of 12 reference sources Mi j — one warm and one
cool source for each camera i. (a) A view of the camera array, seen from the point of view of the object, in which the backsof the reference sources are made visible for clarity. (b) A cross-sectional view of the camera array and reference sources.
The black border indicates the portion of the field of view that is unobstructed for all six cameras.
For a reference source placed a distance z in front of a camera lens of focal length f , the image will occur at a distancez 0 behind the lens, where
1
1 1
= + .
z0
z
f
We will refer to z 0 as the “aperture location”. Many microbolometer cameras use a rather short focal length, so that theobject distance can be approximated as infinite. In this case, the defocus distance becomes z 0 − f , causing a point at theaperture to blur into a circle of radius br = (z 0 − f )/(2 f# ) for a lens with f-number f# . Using p for the pixel size of thedetector, we can express the blur diameter in units of pixels as
bd =z0 − f.
p f#

The blur diameter bd gives the number of pixels in the image that we need to allow between the blurry edge of the apertureand the unblurred image of the reference source. For example, if we use a microbolometer camera with 25 µm pixels, andan f# = 1.25 lens of focal length f = 9 mm, then placing the aperture at a distance of 300 mm in front of the camera array
will produce a blur margin of
9.28 mm − 9 mm
bd == 9.0 pixels .
(2.5 × 10−2 mm)(1.25)
In general, we will want to have an extended region of pixels to view the reference blackbody sources. If we choose toimage the sources into a 5 × 5 pixel region, and allow an error margin of an additional 2 pixels, then the aperture boundary
will reduce the image size by 16 pixels in both the top and the bottom of the image, i.e. a loss of a total of 32 rows ofdata. If the detector array format used in our arrayed cameras are 320×256 format, then adding the aperture for dynamic
calibration will cause a loss of 32/256 = 12.5% of the overall image.

5. CONCLUSION
Although microbolometer thermal cameras are inexpensive in comparison to their cryo-cooled counterparts, they remainmuch more expensive than visible cameras, for the same number of pixels. There are a number of applications — snapshot

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M0

M3

M3A M3B M4A M4B M5A M5B

3

5

4
1

2

ref
B

ref
A

camerablock

M0A M0B M1A M1B M2A M2B

3

4

5

0

1

2

cameras:detectorarray 0detectorarray 3

camerasmirrorsA
B

mirrors

BA0

top row of

bottom ro

w of mirrorsreferencesources
M0A M0B M1A(a)

M3A M3B M4A

(c)

(b)

Figure 2: An example layout for a 2 × 3 array of cameras, using one cool and one warm reference source and an array of
mirrors Mi j : two mirrors j for each camera i. (a) A view of the camera array, seen from the point of view of the object, inwhich the backs of the mirrors are made visible for clarity. (b) A cross-sectional view of the camera array and reference
sources. The black border indicates the portion of the field of view that is unobstructed for all six cameras. (c) A 3D viewof the mirror and camera lens array, as seen from a perspective behind the camera block. (The camera detector cores are
not shown for clarity.)
M6B M7A M7B

M 6A
M4A
M4B
M0A

6

7

4
0

M8A M8B M9A

8
A

1

9
5

B

2

3

M9B

cameras

M 5B
M 5A
M3B

mirrorsreferencesourcesM0B M1A M1B M2A M2B M3A

Figure 3: An example layout for dynamic calibration with a 10-camera array and 20 mirrors.
spectral7 and polarization imaging8 in particular — where the number of pixels is insufficient for doing useful work.9
However, if we can use an array of cameras we can increase the number of pixels available without making extreme
demands on detector manufacturers. For microbolometer cameras, however, radiometric matching between cameras has
been a long-standing problem that has gotten in the way of doing this kind of array imaging. As we have shown above,by carefully designing an aperture to block the edge of the cameras’ field of view, we can insert reference blackbody
sources into the image of each camera and dynamically recalibrate them while collecting measurement data. This enforces
radiometric matching between the cameras, opening up camera arrays to applications that have until now been blocked by
the difficult problem of calibration drift. The tradeoff is a reduction in the available field of view.
In Figures 1 & 2, we show example layouts for an array of six cameras. Other layouts are of course possible, such as
the 10-camera layout shown in Fig. 3. As the number of cameras in the array increases, however, parallax between theindividual cameras’ field of view becomes larger and more difficult to correct. In addition, if we use more than two rowsof cameras in our array (such as the three rows used in Fig. 3, then we have to sacrifice pixels in the left and right sides ofthe fields of view and not just the top and bottom, if we want all of the cameras to have an overlapping field of view.

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6. ACKNOWLEDGEMENTS
The original work for developing dynamic calibration hardware was done in 2014, while the author was employed atRebellion Photonics, Inc., and the method was published in a series of patents.10 Although I would have liked to makeexperimental data available to demonstrate the effectiveness of the technique, this has unfortunately not yet been madeavailable.

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S. Chang and Z. Li, “Single-reference-based solution for two-point nonuniformity correction of infrared focal planearrays,” Infrared Phys. & Technol. 101, 96–104 (2019).
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D. L. Perry and E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng.(8)32(8), 1854–1859 (1993).
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N. Hagen and M. W. Kudenov, “Review of snapshot spectral imaging technologies,” Opt. Eng.(9) 52(9), 090901(2013).
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N. Hagen, S. Shibata, and Y. Otani, “Calibration and performance assessment of microgrid polarization cameras,”
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N. Hagen, R. T. Kester, C. Morlier, J. A. Panek, P. Drayton, D. Fashimpaur, P. Stone, and E. Adams, “Video-rate
spectral imaging of gas leaks in the longwave infrared,” Proc. SPIE 8710, 871005 (2013).
10. R. T. Kester and N. Hagen, “Divided-aperture infra-red spectral imaging system” (2017–2019). US patents 9562849,
9599508, 10444070, 10254166, 10267686.
1.

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