zy Lasers in Surgery and Medicine 10510-523 (1990) Limitations of a Thermal Camera in Measuring Surface Temperature of Laser4rradiated Tissues zyxwvu Jorge H. Torres, MD, Thomas A. Springer, MS, Ashley J. Welch, John A. Pearce, PhD PhD, and zyxw Biomedical Engineering Program, University of Texas at Austin, Austin 78712 Thermal cameras are used in research laboratories to measure tissue temperature during laser irradiation. This study was an evaluation of the accuracy of a 3-5 pm thermal camera and two S 1 2 pm cameras in detecting the maximum temperatures of small targets. The size of the targets was within the range of laser spot diameters which are used for vessel welding, angioplasty, and dermatology. The response to a sharp thermal edge was measured and analyzed for the three cameras, which had a scanning rate of 30 frames per second. The response of the 3-5 pm camera to reference black body targets of different sizes was also studied. It was found that the detector system required an average of 2.44 p s to reach 90% of maximum step response for the S 1 2 pm system and 5.85 ps for the 3-5 pm system. With a 3 x telescope and a 9.5 inch focal distance close-up lens, the 3-5 pm camera underestimated the temperature of targets smaller than 2.0 mm because of its slow detector response. Although the 8-12 pm camera provides more accurate measurements due to its faster detector response, it still underestimates the temperature of targets smaller than 900 pm, when similar magnification and focal distance are used. Methods to compensate for the inaccuracies are discussed, including empirical correction factors and the inverse filtering technique. zyxwvut zyxwvu Key words: infrared camera, tissue temperature, measurement error INTRODUCTION AND BACKGROUND The cameras measure temperature by detecting the infrared radiation emitted by the obThermal cameras have been used in industry jects in their field of view. Objects radiate energy to measure relative temperatures of specific ma- according to their absolute temperature and in terials, and by the military to identify targets. proportion to their surface emissivity. An ideal They have also been used clinically to help in the diagnosis of breast cancer or t o study circulatory problems. These cameras are now becoming more Accepted for publication August 1, 1990. common in laboratories established for biomedi- Address reprint requests to Dr. Jorge H. Torres, Biomedical cal research. In the particular area of laser appli- Engineering Program, Univ. of Texas at Austin, ENS 610, Austin, TX 78712. cations t o medicine, thermal cameras are used to measure tissue surface temperature during laser Dr. A.J. Welch is the Marion E. Forsman Centennial Professor of Electrical and Computer Engineering and Biomedical irradiation. The information obtained is corre- Engineering. lated with the extent of damage observed histowork was supported in part by the Free Electron Laser logically, and provides insight into the kinetics This BiomedicaUMaterials Science Program-ONR contract numand thermodynamics of laser interaction with tis- ber N00014-86-K-0875-and in part by the Albert and Clemsue. mie Caster Foundation. 0 1990 Wiley-Liss, Inc. z zyxwvu Limitations of a Thermal Camera 51 1 black body, a body which absorbs all radiation incident upon it and reflects or transmits none, Detector has an emissivity of 1.0. It also emits the maxi0 mum possible amount of energy at any specific I temperature and wavelength. Most bodies, however, may be described as “gray bodies” with emissivity less than one and approximately indeCamera pendent of wavelength. For example, some polished metallic surfaces have an emissivity as low Target as 0.05, whereas vascular tissues have emissivities from 0.93 to 0.98 [ll. For a “gray body,” the total emissive power (over all wavelengths) is [2]: Fig. 1. a: Detector instantaneous field of view (IFOV = p). I m zyxw zyxwvut zyxwvu zyxwvutsrqponm E(T) = eaT4 (1) where (T is the Stefan-Boltzmann constant, 5.67 X lo-’ (W/m2.K4),and E is the emissivity (0 5 E I11,which is defined as the ratio of the radiant energy emitted by an object at a specific temperature to the radiant energy emitted by a black body at the same temperature. Two infrared spectral bands exhibiting minimum absorption by the atmosphere are used for thermographic imaging: 3-5 pm and 8-12 pm. The detector for the 3-5 pm band is normally a crystal of mercury-cadmium-telluride (HgCdTe) or indium antimonide (InSb). Only a crystal of HgCdTe may be used as a detector for the 8-12 km band owing t o its narrow energy band gap. Due t o the low photon energy of the infrared radiation t o be measured, it is necessary to cool the detector with liquid nitrogen t o -196°C (77 K) in order to minimize thermal noise. In a typical instrument, the electrical conductivity of the detector changes proportionally with the total power of the radiant energy received. A voltage is obtained from a resistance bridge configuration and translated into gray level intensity or color band displayed on a monitor. At each instant of time, the detector can “see” only a certain region which falls within its “instantaneous field of view” (IFOV) or acceptance angle. The IFOV and the distance between the detector and the target determine the spatial resolution of the camera. The smaller the IFOV the better the detector can discriminate between two points, and therefore the better the resolution. To form a complete thermal image, the detector must scan an entire scene. This is accomplished by mechanically scanning the detector either by rotating prisms or oscillating mirrors, resulting in a “flying spot scanner.” The IFOV determines the size of the individually resolvable The diameter of the viewed area w is determined by the IFOV and the distance to the detector D. b Optical path followed by the emitted radiation to reach the detector (Det) inside the camera. samples or independent picture elements. The definition of IFOV is presented graphically in Figure la, and is expressed in the equation: IFOV = p = 2tanp1[w/2D1 (2) where w is the width of the region to which the detector responds at any given instant of time, and D is the distance from the target t o the detector. The distance D includes the optical path internal to the camera as shown in Figure lb. Due to focusing lenses and other optics, an effective distance D’ must be determined for each particular scanner. When the thermal camera is focused on an opaque surface (with zero transmittance), the radiation (radiosity) received by the detector is: where J,(Ts,Te,E) is the measured radiosity, Eb(Ts) is the black body emissive power at the temperature of the surface Ts, and Eb(Te) is the black body emissive power at the temperature of the environment Te, all given in Watts/m2. The surface reflectance p is related t o the emissivity by p = 1 - E. Knowing the radiosity measured by the camera, the temperature of the environment, and the emissivity of the surface, Eb(Ts) can be obtained from equation (3). Once Eb(Ts) is found, the surface temperature Ts can be estimated from calibration tables which use Planck’s law of spectral distribution of energy as a function of temperature [21. Since the relationship between emissive 512 zyxwvutsrqp zyxwv zyxwvutsrqponmlkjih Torres et al. 1500 1 0 50 100 a color monitor. Initial experiments performed with this camera provided tissue temperatures lower than expected during irradiation with small spot size laser beams. In vessel welding experiments using a C02 laser and a spot size of 500 pm, the camera indicated temperatures considered too low for the macroscopic and histologic damage observed. Experiments with argon laser irradiation of human aorta using spot sizes between 700 pm and 1 mm led to a similar observation. Also, there have been some reports on COz laser irradiation of dog aorta and rat femoral and carotid arteries at spot sizes of 200 t o 350 pm [5-71 in which the authors, although using different thermographic imaging systems, have measured temperatures that, in our judgment, may be lower than the actual values. Therefore, we decided to carry out the present study to evaluate the accuracy of thermal cameras in detecting the temperature of targets smaller than 2 mm. In this paper an experimental evaluation of the system response to small targets is presented, and methods to correct for errors are discussed. zyxwvutsrqpo zyxwvutsrqpon zyxwvutsrqp 150 200 250 300 Blackbody Temperature ("C) Fig. 2. Non-linear relationship between band-limited emissive power and black body temperature. (Data were obtained from Ryu L121.1 power and temperature is not linear (31, and since factors like atmospheric absorption and attenuation by filters and other optics in the camera affect the measured radiosity, calibration must be performed for each particular camera in order t o obtain the correct target temperature. The nonlinear relationship between band-limited emissive power and black body temperature for both the 3-5 and the 8-12 pm bands is presented in Figure 2. A table with values corresponding to the curves in Figure 2 can be constructed. For speed in computation, the curves can be approximated by polynomial functions [41. In general, the Calibration method uses two or more reference black bodies at known temperatures whose emissive powers are measured by the camera. Calibration tables are then utilized to estimate the target temperature. In the past few years, in our laboratory, we have used an 8-12 pm camera to measure tissue surface temperature during laser irradiation, with spot sizes usually varying from 700 pm to 2 mm. We calibrated the thermographic images by placing two reference black bodies at known temperatures in the scene close t o the target. The gray scale thermal images were recorded on videotape and subsequently digitized and analyzed on a computer. Using the gray level and temperature values of the black body references as well as the calibration tables [4], the temperature of the target was calculated from its measured gray level (linearly related to its emissive power). More recently however, we acquired a new 3-5 pm thermal camera which uses internal calibration t o calculate and display temperatures on MATERIALS AND METHODS Thermographic Imaging System A 3-5 pm thermal camera model 600L from Inframetrics, Inc., was primarily used for this study. Two 8-12 pm cameras, models 525 and 600L from Inframetrics, Inc., were also tested in order t o compare detector responses. All three cameras use oscillating mirrors to scan the scene horizontally and vertically and produce images at 30 frames per second. The thermal cameras tested in this study use two mirrors oscillating at 3.933 kHz and 60 Hz to scan the scene horizontally and vertically, respectively. Like standard video, the vertical scanning follows a sawtooth waveform and images are produced at 30 frames (or 60 fields) per second. However, the horizontal scanning has a uniform oscillatory pattern instead of the sawtooth form of standard video. Due to the lower frequency and the oscillatory type of the horizontal scanning, each line is scanned in 125 p s (instead of 53 p s of standard video) and two consecutive lines in a field are scanned in opposite directions. The result is that only 7,866 horizontal lines are scanned every second (as opposed to the 15,750 lines of standard video). There are 100 horizontal lines of actual infrared information per field (or 200 per frame), and each line contains 256 digital samples [8,91. The differences between standard zyxw z zyxwvutsrqponml zyxwvuts Limitations of a Thermal Camera 4 53 p e c > < 125 p e c 513 > Black Body Thermocouple Thermal Camera Standard Video Aluminum Shield Thermal Camera (with oscillating mirrors) Fig. 3. Comparison between standard video raster and thermal camera raster. For the thermal camera, horizontal scanning has a uniform oscillatory pattern instead of a sawtooth form typical of standard video. video and thermal camera scannings are shown in Figure 3. A computer digitizes the analog signal from the camera and then displays it on a TV monitor. In order to match video standards, the digital information is loaded into a FIFO (First In First Out) memory for the right-going scan, and into a LIFO (Last In First Out) memory for the leftgoing scan. While the camera scans one line, the information stored from the previous line is read twice out of memory and displayed twice on the TV monitor in order to generate the 15,750 lines per second of standard video. The final video image contains 400 lines of infrared information with 256 pixels per line. The rest of the 525 TV lines are used for text and gray scale display. Since 256 digital samples are taken during the scanning of one horizontal line and 7,866 lines are scanned every second, the camera bandwidth is: Bandwidth = 7,866 linedsec X 256 sampledine = 2.01 MHz. The cameras have a total horizontal field of view of 18"t o 20" (314 to 350 milliradians). The instantaneous field of view (IFOV) is 2mRad for the 8-12 pm cameras and 3.5 mRad for the 3-5 pm camera [8,9]. Therefore, although sampling is performed 256 times during a horizontal scan, there are only 175 (350 mW2 mR) independent samples in a line for the 8-12 pm system, and 100 (350 mW3.5 mR) for the 3-5 pm system. The manufacturer specifies a minimum detectable temperature difference of 0.1"C for the 8-12 pm cameras and 0.2"C for the 3-5 pm camera [S]. Each of the three cameras uses a mercurycadmium-telluride detector which has a specified time constant of 0.5 t o 1 ps [lo]. zyxwv Black Body Aluminum Shield Fig. 4. Experimental setup to measure the response to a thermal step. Experimental Evaluation A) System response to a thermal step. For small targets, the accuracy of the temperature measurements depends on the detector IFOV and slew rate. These parameters were assessed by measuring the detector response t o a sharp change in temperature or step during horizontal scanning. A temperature step was created by taking a 2 inch circular black body and covering half of its surface with a shield of aluminum foil as shown in Figure 4. In this way, during horizontal scanning, the detector initially saw "room" temperature reflected by the aluminum foil, and at the edge of the foil it saw a sudden, sharp change to the temperature of the black body which was electrically heated to a known temperature. The edge of the aluminum foil was made as sharp and straight as possible t o avoid blurring effects. Each camera was placed at 9.5 inches from the black body and focused t o obtain the sharpest image of the edge. The images were recorded on videotape in gray scale for further analysis. No telescope or external optics were used with the cameras. One hundred percent field of view was used (no zoom), providing a total horizontal view of approximately 11 cm. The response was evaluated for three temperature steps: 25-36.2"C, 25-52.4"C, and 35-105°C. Images were digitized on an Intel Computer iSBC 86/30 and values of gray level were obtained for each pixel in a selected subframe centered at the edge. Minimum and maximum gray levels were determined by averaging the value of 10 pixels on a particular line in the cold area before the step and in the hot area after zyxwvutsrqp zyxwv Torres et al. the step respectively. Several lines were analyzed Determination of the Camera Point in order to find a typical response curve for both Spread Function 514 right-going (cold-to-hot) and left-going (hotto-cold) scans. During the experiments, an oscilloscope was used to corroborate detector rise time and curve shape. In order to evaluate the effects of using a telescope and a close-up lens on the detector response to the sharp thermal step, another set of experiments was performed with the 3-5 pm camera. The camera was used with a 3~ telescope and a 9 inch close-up lens and was focused at 9.5 inches (24.13 cm) from the sharp edge. The 25-52.4”C thermal step was used in this case. Computer analysis similar to that described above followed the experiments. B) Camera temperature readings for small targets. The accuracy of the 3-5 pm camera in measuring the maximum temperature of small black body targets was evaluated by placing a variable slit in front of a black body with a 1.6 mm circular aperture. This camera had internal calibration and provided a temperature reading for the target. The black body was electrically heated and a thermocouple measured the temperature of its cavity. The width of the slit could be varied from 0.1 to 1.6 mm. A 3 x telescope and a 9 inch close-up lens were used. The camera was placed at 9.5 inches from the slit so that the best focus was obtained. The black body was maintained at 100°C for easy reference. For each width of the slit, the maximum temperature read by the camera was recorded. To compare with these experiments, two black bodies with sizes of 0.5 and 1.0 mm respectively were made by drilling two holes of corresponding diameters in an aluminum block. The holes were deep enough (16mm) to make the cavities approximate ideal radiators. The surface of the aluminum block was highly polished. The block was heated slowly by a hot plate, while thermocouples placed at the ends of the cavities measured the corresponding temperatures. The temperatures read by the 3-5pm camera were compared with those measured by the thermocouples. In addition, temperature readings for a separate black body with a 2 mm diameter were also tested. To evaluate the system response as a function of target temperature, the black body size was kept constant at 0.5, 1.0, and 1.5 mm (fixed slit width) while varying the temperature from 30” to 150°C. Target temperatures and the corresponding temperature values measured by the 3 5 pm camera were recorded and compared. The image degradation effects caused by a particular imaging system (in this case a thermal camera) can be assessed by measuring the point spread function (PSF)of the imaging system. The PSF is the response of the system to a point source input. Considering that the image is a two-dimensional distribution of point sources, knowledge of the PSF can be used to determine the action of the system on the image [lll. For a thermal camera, the detector response as well as the scanningmechanism and the optics involved produce a degradation action or blurring operation on the input picture. Calling this blurring operation (i.e., point spread function) h(x,y), the input image f(x,y), and the output (degraded) image g(x,y), then: where * indicates 2-D convolution. If the input picture is only a hot point source, the output will be the PSF of the camera. In practice, for a thermographic imaging system with limited spatial resolution, the dimensions of a hot point source which could be used to determine the PSF are difficult to define. However, the following method can be used to find the point spread function h(x,y) of the camera [4,111: The system response to an edge or thermal step can be measured in the way described in the previous section (see Fig. 4). The system response t o a sharp edge oriented in a particular direction is defined as the “edge spread function” (ESF) for that particular direction or h,(x,y). The derivative of the ESF in any direction is the “line spread function” (LSF) in that direction or hL(x,y). In other words, the LSF is the system response to a line oriented in the direction of the edge described above. The projection of the LSF is basically a point. Experimentally, the thermal edge can be rotated 360” in small steps (which depend on the precision wanted) and the ESF can be measured for different orientations. The corresponding LSFs can be then calculated. The projections of the LSFs taken at different orientations (defined by an angle 8 + 90”) allow the two-dimensional reconstruction of the point spread function. See Figure 5 for a graphical summary of this process. The reconstruction of the PSF from the projections of the LSFs is based on the “Fourier Slice Theorem” ill3 which states that the one-dimensional Fourier transform of the projection of the zyxwv zyxw - zy zyxw metry, this final LSF was rotated 360" to obtain the camera PSF. + zyxwvutsrqp zyxwvutsr zyxwvuts Gaussian Vs. Uniform Targets A Edge Spread Function (ESF) Line Spread Function (LSF) Point Spread Function (PSF) Fig. 5. Method to obtain the point spread function from the projections of the line spread functions a t different orientations. image function (in this case the PSF) along a line s oriented at 0 + 90" is equal to the two-dimensional Fourier transform of the function along a line t oriented at an angle 0 from the horizontal axis x (see Fig. 5). A reconstruction algorithm like the filtered-backprojection method [ 111 can be used. In this study however, a more simplistic approach was taken to get the PSF for the 3-5 pm thermal camera. First of all, due t o the way the scene is scanned and the way the data are stored and displayed, the PSF is asymmetric. Despite that fact, since the detector response during the horizontal scanning is the most limiting factor for the peak temperature measurements, only the ESF and the LSF for 0 = 0 (vertical edge) were measured in this study. Then, the PSF was constructed assuming circular symmetry by rotating 360" the projection of the LSF for 0 = 0 (see also Springer et al. [121). The PSF indicates the blurring effect of the camera on a thermal image. Once the PSF is known, restoration (to a certain degree) of an original thermal image is possible from the camera output. In this investigation, the PSF of the 3-5 pm camera model 600L was measured. Ryu [41 had measured the PSF for the 8-12 pm camera model 525, also tested in this study. Since the response of the 3-5 pm camera to a cold-to-hot step (right-going scan) was different from its response to a hot-to-cold step (left-going scan), as will be shown later, the following procedure was used to establish a PSF for this camera: Ten lines were selected for each scan direction. For each line, median filtering was applied to remove the noise, and then the edge spread function (ESF) was differentiated to obtain the corresponding line spread function (LSF). The ten LSFs were averaged together t o produce one LSF per scan direction. The two LSFs, one for the right-going scan and one for the left-going scan, were again uniform (pulse type) temperature distribution across the cavity. However, before heat conduction becomes significant, most temperature rises in tissue during laser irradiation have a gaussian distribution (which has smoother edges and is not uniform across the spot). In order to compare the system response to gaussian targets with the response to uniform targets of corresponding diameters, the following procedure was used: Targets with uniform and gaussian temperature distributions were simulated on a computer, and the PSF previously obtained for the 3-5 pm camera was used to calculate the camera response to the peak temperature of the targets. For each target type, the size (diameter) in pixels was varied. The width of the uniform rectangular targets was taken as the diameter. For the gaussian targets, the diameter was the distance between the points at which the temperature dropped to l/e2of the central value. Once the onedimensional temperature distribution was simulated, a fifth-degree polynomial approximation to the 3-5 pm band-limited power vs. black body temperature curve was used to obtain the emissive power distribution which was subsequently normalized to values from 0 to 100%.The normalized emissive power distribution (EJ was then convolved with the camera one-dimensional PSF to obtain the system response (E,) in percentage, or: Ei * PSF = E,. For the uniform targets, system response was assumed to be independent of the magnitude of the thermal step, and a thermal step from 0 to 100°Cwas arbitrarily chosen. Since the shape of the gaussian distribution varies with the peak temperature, three peak temperatures were selected for comparison: 50, 100, and 150°C. RESULTS System Response to a Thermal Step The detector response t o a thermal step from 25 to 36.2"C is shown in Figure 6 for the three cameras. The graph was normalized from the average background gray level t o the maximum gray level achieved by each camera. It represents the percentage of the system maximum response as a function of scanned pixels in a displayed TV Torres et al. 516 zyxw Large hot object , , 1 2 0 3-5 pm Camera Model 600L 8-12pm Camera Model 600L 8-12 Vrn Camera Model 525 , , 3 4 , l l l l l l 5 6 7 8 9 1 0 1 1 Time (psec) Maximum. 0 objec! zyxwvuts zyxwvutsrq zyxwvutsrqpon zyxwvutsrqponmlk l 0 A Small hot , Fig. 6. Detector response to a 25-36.2”C thermal step for three thermal cameras. Note the slower response of the 3-5 km detector. line consisting of 256 pixels (upper scale), and as a function of time (lower scale). In this way, the relationship between time and pixels scanned on a horizontal line can be observed as the system responds t o the cold-to-hotstep. Since a line of 256 pixels is scanned in 125 ps, each pixel is scanned in approximately 0.49 ps. As seen in Figure 6, all three systems take some time and several pixels in the scanning line to reach maximum response. The 8-12 pm detectors require 2.44 p s to reach 90% of the maximum response, which corresponds t o 5 pixels. The 3-5 pm detector system is slower than the 8-12 pm system, requiring 5.85 p s or 12 pixels, to reach 90% of the maximum response. In the case of the 3-5 pm thermal camera, when the 3~ telescope and a close-up lens with 24.13 cm (9.5 inch) focal distance are inserted, the measured horizontal viewing distance is 3.0 cm and each pixel corresponds t o 117 pm (3.0 c m / 256). This means that the detector needs t o scan 1.4mm in the scene to reach 90% response and 2.0 mm to reach 100%response. Therefore, it will scan through any hot object smaller than 2 mm without reaching maximum response. The system will then indicate a temperature value lower than the actual temperature of the object. A graphical representation of the problem is shown in Figure 7. In the case of the 8-12 pm system, response time is still a problem but it is less pronounced. Based on Figure 6, if the 8-12 pm camera with the same telescope and close-up lens is also focused at 9.5 inches from the target, the system will not indicate the correct temperature for ob- .. .. Time Cletector Response (Apparent Intensity) Fig. 7. Sketch to show that the detector does not reach maximum response while scanning small objects. jects smaller than 900 pm (about 8 pixels), although it will reach the 90% response rate for a 550 pm object (about 5 pixels). Numbers obtained for both 8-12 and 3-5 pm detector responses are presented in Table 1. The detector response to the hot-to-cold step or sudden temperature drop was measured by following the left-going scanning lines. Gray level values fell from 90% t o 10% of the maximum value in approximately 1.5 p s for the 8-12 pm system and 2.5 p s for the 3-5 pm system. Therefore, for the 3-5 pm camera, the response to a sudden temperature drop was more than two times faster than the response to a sharp temperature increase: 2.5 p s (for 90-10%) vs. 5.15 p s (for 10-90%). For the 8-12 pm camera, the difference between these two responses was much less pronounced: 1.5 p s (for 90-10%) vs. 2.0 p s (for 1090%). During scanning, the detector response t o rapid temperature changes in the scene depends on two factors: the detector slew rate and its instantaneous field of view (IFOV). Looking at Figure 6, one can see that the detector response curves have a lower slope for the first 1or 2 pixels. The detector appears very slow to respond when it first “sees” the thermal edge. This is actually a blurring effect caused by the detector IFOV and is more pronounced for the 3-5 pm camera. The effect of the IFOV is described in Figure 8. When the detector first encounters the edge, it receives zyxwvut zyxwvu Limitations of a Thermal Camera TABLE 1. Detector Responses Detector parameter Time constant (0-63.2%) Rise time (10-90%) Time for 0-90% response 8-12 pm system 1.6 2.0 2.44 517 3-5 pm system 2.2 5.15 5.85 0 2 4 zyxwvutsrq zyxw 6 8 10 12 14 16 18 20 22 24 Pixels Fig. 9. Comparison between detector response when telescope was used and response when only standard optics were utilized. clF[m __.. __.. --..- = - F zyxwvut recall that the IFOV determines the spatial resolution of the system. When a 3 x telescope and a close-up lens with a 9.5 inch focal distance are used, an IFOV of 2 mRad corresponds to a distance of 200 pm and an IFOV of 3.5 mRad corresponds t o 300 pm, while a pixel displayed on the monitor corresponds to 117 pm. In this case, the response to a target 5250 pm is predominantly affected by the IFOV. For targets larger than 250 pm, the detector slew rate is the most limiting factor in the response. Mathematical expressions for the response to an edge, based on the IFOV alone, can be obtained for a circular window and other geometries. The magnitude of the thermal step did not seem t o affect the detector response. The responses of the 3-5 pm detector to three different thermal steps were almost identical to the response shown in Figure 6. There was basically no difference between the curves for the 25-36.2"C step, the 25-52.4"C step, and the 35-105°C step. The effect of the telescope and close-up lens on the response t o the edge was also tested. In Figure 9, the response t o the 25-52.4"C thermal step when the 3 x telescope and the 9 inch closeup lens were used is compared with the response t o the same step when only standard optics were utilized. The response was slightly slower when the telescope and close-up lens were used, perhaps due to some blurring of the edge by optical magnification. With the camera focused at 9.5 inches, the entire image was magnified 3.67 times (from a total horizontal view of 11 cm down t o 3 cm). For small objects, of course, a telescope and a close-up lens are required. That arrangement zyxwvutsrq Displayed Pixels Fig. 8. Description of the effect of the instantaneous field of view (IFOV) on the response to an edge. Note the overlapping of sampled IFOVs when they are larger than the distance between consecutive samples. energy from an area covering both sides of the edge. The dimensions of this area depend on the IFOV. The larger the IFOV the longer it takes for the detector to "move" completely from the cold zone to the hot one. In addition, since the total horizontal view is 350 mRad, and since 256 digital samples are taken during the scanning of one line, sampling is performed every 1.37 mRad. This means that if the IFOV is larger than 1.37 mRad, overlapping of consecutive sampled IFOVs occurs and the corresponding displayed pixels are not independent. The result is blurring and reduced image resolution, The larger the IFOV the worse the blurring effect. This effect is present in the response of the cameras tested here because the IFOV is 2 mRad for the 8-12 pm detector and 3.5 mRad for the 3-5 pm detector [91, while the pixels displayed on the monitor correspond t o the digital samples taken every 1.37 mRad. Therefore, for the 8-12 pm camera, totally independent samples are displayed every 2 pixels; and for the 3-5 pm camera, completely independent samples are displayed every 3 pixels. It is important to zyxw zyxwvutsrqponml zyxwvu Torres et al. 518 140 -0- 100 4 ...................................,........................... NoTelescope 3X Telescope + 9close-up lens 100 2ofi-, ' zyxwvu " 1 zyxwvutsrqpon , 0 0 1 2 3 4 5 6 7 8 Pixels 9 , , 1011 1 2 1 3 1 4 1 5 Fig. 10. Effect of magnifying a 0.5 mm black body with a 3 x telescope and a 9 inch close-up lens on the intensity measured by the 3-5 km system. The arrows indicate the slow response at the edges due to the effect of the IFOV. magnifies the image, improving the resolution and allowing the detector to respond better t o small targets, since they now include more pixels. The improvement in the response of the 3-5 pm camera t o a 0.5 mm black body target at 137°C when the telescope and close-up lens are used can be observed in Figure 10. The arrows indicate the slower response at the edges of the black body due to the effect of the IFOV. Camera Temperature Readings for Small Targets The apparent temperature measured by the 3-5 pm thermal camera focused on a black body at 100°C as a function of black body size (slit size) is presented in Figure 11. The camera with telescope (3x ) and close-up lens was focused at 9.5 inches from the target. It is easy to see that the camera underestimated the temperature of the target for all sizes up to 1.6 mm. The smaller the target size the worse the temperature underestimation. These data confirm that the system is unable to reach its maximum response while scanning objects smaller than 2 mm. In Figure 11, note that for a target size of 500 pm the camera read 65°C instead of lOO"C, and for a 1.0 mm target the camera read 85°C. When the camera was focused on the black bodies made in the aluminum block, it read 62°C and 86°C for the 0.5 and 1mm black body respectively while the cavity thermocouples read 100°C, clearly in agreement with the values plotted in Figure 11.On the other hand, the camera provided the correct temperature for the 2 mm black body. The system response as a function of target 00.0 0.2 0.6 0.4 0.8 1.0 1.2 1.4 1.6 Target Size (mm) Fig. 11. Apparent temperature measured by the 3-5 pm camera as a function of black body size. The black body was maintained at 100°C. temperature was also evaluated by varying the temperature of a fixed size black body. The 3-5 pm thermal camera was again used to measure the temperature of the target. A ratio of the measured temperature rise ("(3) t o the actual temperature rise ("C) as a function of the actual target temperature above that of the environment ("C)is presented in Figure 12a for three different target sizes: 0.5, 1.0, and 1.5 mm. As can be seen in the figure, this ratio increases as the target temperature is increased. The non-linear relationship between band-limited emissive power and black body temperature explains this behavior (see again Fig. 2): as temperature increases, a particular emissive power difference corresponds to a smaller temperature difference. Note that, for the range of temperatures investigated, the ratio increases with temperature in a linear fashion. After curve fitting, linear functions with approximately the same slope were obtained for the three cases (see the mathematical expressions in Fig. 12a). After averaging the slopes, the following relation was obtained: z = b + 0.25 AT (5) where z is equal to 100 times the fraction AT measured ("C)/AT actual ("C), b is a constant which depends on the target size, and AT is the actual temperature rise ("C) with respect to the ambient temperature. If, due t o some calibration error, the camera provides a different value for the ambient temperature when changing temperature scales, zyxwvutsr R”2 = 0.98 519 The value of b for the 2 mm black body (also used in the test) was included in Figure 12b, consider100 ing that the camera provided the correct temper90 56.746 + 0.25319 AT ature at AT of 40°C. I1 80 Therefore, for temperature rises up t o 120”C, 5x 70 34,890 o,25240 AT an empirical correction factor z has been derived 2 6 0 for the 3-5 pm camera used in this study, and 50 equations (5) and (6) can be used to estimate the 40 1.5 mm actual temperature of targets smaller than 2 mm. Higher target temperatures were not tested due I.Om to limitations in the black bodies used in our 0 0.5 mm study. These black bodies could not be heated 10 more than 150°C. Computer simulations using a 0 0 20 40 60 80 100 120 140 the relationship between band-limited emissive AT actual (“C) power and temperature (shown in Fig. 2) indicate that the linearity presented in Figure 12a does b = - 37.565 + 240 19s - 261 4 7 s V + 159 86sA3 - 4 8 . 1 4 7 ~ ~+45 ,767553 R”2 = 0.99 not hold at higher temperatures, and that a more loo complicated expression for the correction factor is 90 required. However, for a limited range of temper80 atures, it is possible t o obtain a simple expression 70 for a correction factor which allows an approxiD 60mation to the true target temperature, as it was c done in this study for temperatures from 25°C to 50 4> 40 150°C. The manufacturer provides a graph for a 30 function called “slit response function” (SRF), 20 which is basically the fraction AT measured/AT 10 actual for a vertical slit target of various widths as measured experimentally [81. However, as b 0.0 0 . 2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 shown above, this fraction changes with temperTarget size (mm) = s ature and does not have a constant value. We Fig. 12. a: Ratio of measured temperature rise to actual tem- have found that the values of the SRF indicated in perature rise as a function of target temperature above am- the manufacturer’s manuals hold only for target bient temperature for three different black body sizes. In all temperatures around 100°C (AT around 75°C). It three cases, note the linear increase in this ratio with increasing temperature. b: Value of the constant b as a function of will be more accurate t o follow the procedure target size. This value will be used in the equation z = b + shown above to derive a correction factor for a 0.25 AT, where z will be the correction factor (%). particular thermal camera. z = 71.041+ 0 . 2 4 2 7 0 ~ ~ N + 2 5 : z zyxw zyxwvutsr zyxwvutsrqponmlkjih zyxwvutsrqpon zyxwvutsrqp zyxwvuts zyxwvutsrqpon Limitations of a Thermal Camera s. ’ 0 Camera Point Spread Function the offset must be taken into account. Based on the curve of apparent temperature vs. target size for a black body at 100°C (Fig. ll),the values of z were obtained for target sizes from 0.2 t o 1.6 mm at a AT of 75°C. Using equation (5), the corresponding values of b were obtained. These values are plotted in Figure 12b. A fifth-degree polynomial function fitted those points extremely well, allowing the use of the following expression t o estimate b for a specific target size: b = -37.56 zyxwvu + 240.19 s - 261.47 S’ + 159.86 s3 48.15 s4 + 5.77 s5 (6) - The PSF obtained for the 3-5 pm camera is shown in Figure 13. In this three-dimensional figure, the x-y plane represents space divided in pixels, and the height (z direction) corresponds to the normalized response. As indicated in the Methods section, the line spread functions for the rightgoing scan and for the left-going scan were averaged together and the result rotated 360”. where s is the size of the target in millimeters. Gaussian Vs. Uniform Targets The PSF presented in Figure 13 was used to predict the response of the 3-5 pm system t o simulated targets with either gaussian or uniform temperature distribution. The predicted responses to both target types were then compared. Only 520 zyxwv zyxwv zyxwvutsrq -- Torres et al. Rectangular Gaussian 3 0 zyxwvuts zyxwvut zyxwvutsrq 5 7 10 15 20 25 30 35 Diameter (pixels) zyxwvutsr r n 0 .35 S 8 . 8 2 1.17 x s 1 I 1.76 2.34 2.93 3.51 4.10 Diameter (m) Fig. 13. Point spread function (PSF)obtained for the 3-5 pm camera. The x-y spatial plane is divided in pixels. The height z indicates the system normalized response. Fig. 14. Comparison of the 3-5 pm system response to gaussian targets with the response to uniform rectangular targets of corresponding diameters. The targets were computer simulated and the PSF was used for the calculations. one-dimensional computer analysis was performed. The PSF was convolved with the normalized emissive power resulting from the simulated temperature distribution. In Figure 14, the system response t o targets with uniform rectangular temperature distribution is compared t o the response to targets with gaussian temperature distribution for several target sizes. The graph indicates the percentage of system response t o the peak power emitted by the target (which corresponds to the peak temperature in the simulation). As can be seen, the response is much lower for the gaussian targets than for the rectangular targets of corresponding diameter. Up t o a diameter of 10 pixels, the response to the gaussian target was about half the response to the rectangular uniform target. The calculated response t o gaussian targets is presented in Figure 15 for three different peak temperatures: 50, 100, and 150°C. For similar diameter, the higher the temperature (sharper gaussian) the worse the response. It should be emphasized, though, that all these are responses (in percentage) t o peak emissive power from the target, and that, due t o the non-linear relationship between power and temperature, the percentages do not necessarily hold for corresponding temperature rises. atures of targets which are large and have slow temperature variations, their accuracy is less for small targets or rapidly changing temperatures. Limitations are specified to a certain extent by the manufacturers, but are often overlooked by researchers. Particularly demanding conditions are those occurring during tissue irradiation with small-size laser beams for very short periods of time. This study was directed toward evaluating the accuracy of a camera in measuring the temperature of small and fast-changing targets like those occurring in many medical laser applications. The study was initiated after experimental work produced concern in our group about the accuracy of some thermal measurements. The detector rise time (10-90%) was found to be 2.0 ps for the 8-12 pm camera and 5.15 p s €or the 3-5 pm camera. The response time from 0 t o 90% of the step was 2.44 ps for the 8-12 pm system and 5.85 ps for the 3-5 pm system. It is clear that the 3-5 pm system is more than two times slower than the 8-12 pm system. This makes the 3-5 pm cameras particularly susceptible to errors when measuring temperatures of small targets. The 3-5 pm thermal camera, which produces images at 30 frames per second, requires an object 18 pixels wide (out of 256 pixels in a line) in order to provide the correct temperature. Thus, DISCUSSION the object must cover 7% of the monitor screen Thermal cameras are being used in bio- horizontally. This corresponds t o 2.0 mm when medical research laboratories t o estimate tissue the 3 x telescope is mounted and a close-up lens is surface temperature during laser irradiation. Al- used t o focus the camera at 9.5 inches (24.13 cm) though the cameras accurately measure temper- from the object. A detector response of 90% can be zyxwv zyxwvu zyxwv Limitations of a Thermal Camera 521 obtained for a target of 1.4 mm. Strictly speaking speeds. For example, some systems produce imhowever, for objects less than 2.0mm, the tem- ages at 12.5 frames per second, and even at four perature is underestimated. This was confirmed frames per second. Since the scanning time for by the experiment with the black body of variable one horizontal line is longer, the detector can size heated at 100°C. The camera measured 65°C reach a higher response for small targets, and for the 500 pm black body and 85°C for the therefore the accuracy improves. However, al1.0 mm black body. The accuracy is improved if a though slower scanning systems are spatially close-up lens with shorter focal distance is used, more accurate, they have a poorer temporal rebecause objects appear larger in the scene and the sponse. In many cases of laser irradiation of tisdetector can reach a higher response during hor- sue, very short exposure times are used. In vessel izontal scanning. In general, image magnification welding for example, pulses of 100 ms are typical. with telescopes and close-up lenses improves the With a scanning rate of 30 frames per second, six resolution and the accuracy of the measurements. fields will be scanned during this period of time, An electro-optical zoom feature is also available while with a rate of 12.5 frames per second less in this type of camera. This option reduces the than three fields will be scanned, and it will be horizontal field of view by reducing the amplitude easier to miss the peak temperature that occurs of the horizontal mirror scanning. In this way, the before the laser is turned off. Therefore, there is image is magnified while the scene is scanned at always a trade-off between spatial accuracy and lower speed. However, the detector instantaneous temporal resolution. A system at 4 frames per secfield of view (IFOV) does not change. The zoom ond is extremely accurate for small targets, but only reduces errors associated with detector rise cannot be used for rapidly changing thermal time, and it does not improve errors due to the events like those associated with laser irradiation IFOV. The rather slow detector response from 80 of tissue. to 100%of its final value t o a step change in temFor objects smaller than 250 pm (about 2 perature, as illustrated in Figure 6, further de- pixels), the dimensions of the detector’s IFOV are grades the improvement in measurement accu- critical for the accuracy of the temperature mearacy for small objects which is attributed to the surements. The smaller the IFOV the better the zoom feature. accuracy. In most laser applications, gaussian beam In cases such as vessel welding with CO, laser (10.6 pm wavelength), the 8-12 pm cameras profiles (not uniform profiles) occur. Initially, becan “see” reflected laser radiation, and therefore, fore heat conduction becomes significant, these the 3-5 pm cameras must be used t o measure gaussian beam profiles cause tissue temperature tissue temperature. Considering the slow re- rises with the same gaussian distribution. Using sponse of the 3-5 pm detector, tissue temperature the point spread function obtained for the 3-5 pm measurements during vessel welding with CO, camera, the system response t o computer-simulaser are likely to be inaccurate, since the spot lated gaussian targets was found to be about half sizes normally used vary from 200 to 500 pm. Of the response to uniform targets of corresponding course, the effects of heat conduction must be sizes. Therefore, less accuracy is expected for gaussian temperature profiles with small diametaken into account and will be discussed later. ters (< 3 mm). However, in most cases of laser If other lasers different from the C02 laser irradiation of tissue, heat conduction becomes sigare used for tissue irradiation, the 8-12 pm thernificant after 10 to 100 ms 1141. Radial heat conmal cameras are recommended, considering that their detector system responds faster, producing duction leads to an expanded area of tissue temsharper images and providing more accurate tem- perature rise with a smooth profile. The camera peratures for small spot sizes. Besides, this imag- then “sees” a target larger than the original laser ing band has a more nearly linear relationship beam size, and the overall accuracy greatly imbetween radiant energy and temperature [3,131. proves. Heat conduction makes the analysis of the The 8-12 pm camera provides correct tempera- error in the temperature measurements even tures for targets 2900 pm when focused at 9.5 more complicated. Knowledge of the size of the inches (using the same telescope and close-up lens thermal profile (better than the laser spot size) is described above), with 90% detector response for of primary importance to determine the magnitude of the error and to apply correction factors. targets of 550 pm. In general, reports on temperature measureOther imaging systems (different from the one used in this study) scan the scene at lower ment during CO, laser irradiation of arteries with zyxwvuts 522 Torres et al. small spot sizes [5-71 must be taken cautiously, since the actual tissue temperatures may have been much higher. That includes temperature measurements during vessel welding. Also in relation to temperature measurement during COz laser irradiation, Pearce et al. 131 have called attention to another important factor that affects the measurements: the thermal gradient along the beam. They have shown that, in the case of tissue heated by lasers with very high absorption coefficients like the COz laser, the temperature gradient in the direction of propagation may have a significant effect on the emitted radiation, and therefore affect the thermal camera temperature measurement. Thermal gradients within tissue to a depth of 50-100 pm are important because the detector receives radiation from these internal regions of the tissue. Calibration methods for the camera are based on constant tissue temperature conditions. If significant thermal gradients exist in the first 100 pm below the surface, the camera measures a temperature significantly lower than the actual temperature at the surface of the tissue. Pearce et al. provide a correction factor t o be multiplied by the measured emitted power. This correction factor is (a + p.)/p, where a is the absorption coefficient of the tissue at the laser wavelength, and p is the extinction coefficient of the imaging pass band of the camera. They have calculated a correction factor as high as 3.64 when the 3-5 pm camera images arterial wall during C 0 2 laser irradiation. As a rule, the accuracy of any thermal camera must be tested prior to its use for measurements of tissue temperature during laser irradiation. Empirical correction factors can be obtained for a specific range of temperatures. In this study, a correction factor was derived for our 3-5 p.m camera, on the 25-150°C temperature range, from the experimental data plotted in Figure 12a. By using this factor, the actual target temperature can be estimated from the measured temperature once the target size is known. It is important to point out that, due to individual variability in detector response time and detectivity, a particular expression for an empirical correction factor must be derived for each particular camera, and that it is unlikely that equations (5) and (6) can be applied t o another device of the same model. A more precise technique, although difficult to implement, recovers the original image by digital processing of the degraded image given by the camera. The actual thermal image is “blurred” or zyxw degraded by the camera response which acts like a “blurring filter.” If the camera response is known, an “inverse filter” can be used to recover the actual image from the blurred one. For this reason, the technique is called “inverse filtering.” To create the “inverse filter,” it is first necessary t o find the point spread function h(x,y) of the camera. In simple terms, the theory behind this method is the following: As discussed previously, the resulting output image from the camera is described as: where f(x,y) is the unblurred original image, h(x,y) is the system point spread function, and g(x,y) is the blurred output image. Transforming the above operation from the space domain to the frequency domain we obtain: zyxwvut zyxwvu G(u,v) = F(u,v) H(u,v) (7) where G(u,v), F(u,v) and H(u,v) are the Fourier transforms of g(x,y), f(x,y)and h(x,y) respectively. H(u,v) is called the “optical transfer function.” The original image can be recovered by multiplying G(u,v) by the inverse of H(u,v) in the frequency domain, and then transforming the result back to the space domain: The expression l/H(u,v) = I(u,v) is called the “inverse filter.” Since I(u,v) becomes very large or is not defined when H(u,v) approaches zero, special manipulation of this filter is necessary. Springer et al. [121 have developed a computer algorithm which uses this technique t o restore original thermal images of small targets from gray scale images obtained with a thermal camera. Targets with smooth gaussian shapes, typical in laser applications, are handled better by the program than targets with sharp thermal edges. In general, peak temperatures can be recovered to a close approximation by this technique. The algorithm implemented by Springer can be used with any image processing system and provides the researcher with a tool to improve the accuracy of thermal camera measurements. zyxw z zyxwvutsrq Limitations of a Thermal Camera 50°C 100°C 150°C . 0 . 523 ablation of normal and atherosclerotic human aorta in vitro: a first thermographic and histologic analysis. Circulation 1987; 76:1353-1563. 2. Incropera FP, DeWitt DP: “Fundamentals of Heat and Mass Transfer,” Second Edition. New York: John Wiley & Sons, 1985. 3. Pearce JA, Welch AJ, Motamedi M, Agah R: Thermographic measurement of tissue temperature during laser angioplasty. In Diller KR, Roemen RB (eds): “Heat and Mass Transfer in the Microcirculation of Thermally Significant Vessels.” Anaheim, CA: ASME, HTD, December 1986, vol 61, pp 49-54. 4. Ryu ZM: The effect of nonlinear filtering on the resolution of calibrated thermographic images. Ph.D. Dissertation, The University of Texas at Austin, May 1986. 5. Mnitentag J , Marques EF, Ribeiro MP, Braga GA, Navarro MR, Veratti AB, Armelin E, Macruz R, Jatene AD: Thermographic study of laser on arteries. Lasers Surg Med 1987; 7:307-329. 6. Kopchok GE, White RA, White GH, Fujitani R, Vlasak J, Dykhovsky L, Grundfest WS: C 0 2 and argon laser vascular welding: Acute histologic and thermodynamic comparison. Lasers Surg Med 1988; 8:584-588. 7. Sorensen EMB, Thomsen S , Welch AJ, Badeau AF: Morphological and surface temperature changes in femoral arteries following laser irradiation. Laser Surg Med 1987; 71249-257. 8. Inframetrics, Inc.: “Model 600 IR Imaging Radiometer.” Operations manual. 9. Inframetrics, Inc.: “Model 600L IR Imaging Radiometer.” Operator’s manual. Summer 1989. 10. Vanzetti R: “Practical Applications of Infrared Techniques.” New York: Wiley-Interscience publication, John Wiley & Sons, 1972. 11. Rosenfeld A, Kak AC: “Digital Picture Processing,” Second Edition. 1982, Vol 1. New York: Academic Press. 12. Springer TA, Torres JH, Welch AJ, Pearce JA: Thermal image restoration by the inverse filtering technique. IEEE IMBS 11th Annual International Conference. November, 1989. 13. Diller KR, Pearce JA, Valvano JW, Welch AJ, Wissler EH: Heat transfer: what’s new in bioengineering. SOMA 2(2): 14-21, July 1987. 14. van Gemert MJC, Welch AJ: Time constants in thermal laser medicine. Lasers Surg Med 1989; 9:405-421. zyxwvutsrqponml zyxwvutsrqpo , . . .35 .58 .82 1.17 1.76 2.34 2.93 3.51 4.10 Diameter (mm) Fig. 15. Calculated response to gaussian targets as a function of target size for three different peak temperatures. CONCLUSIONS Infrared camera temperature measurements of laser-irradiated tissue are subject t o several errors which lead to temperature underestimation. For small targets, special attention must be given to the detector instantaneous field of view as well as to the detector rise time relative to the scanning velocity. Each thermographic imaging system must be tested to determine its accuracy and limitations. By using empirical correction factors or, more properly, the “inverse filtering technique,” it is possible to compensate for the errors and to approximate the actual target temperatures. REFERENCES 1. Welch AJ, Bradley AB, Torres JH, Motamedi M, Ghidoni JJ, Pearce JA, Hussein H, O’Rourke RA: Laser probe zyxw