2.1. Method for Calibrating the Temperature of the Blackbody
During the design process of blackbody surface sources, a temperature discrepancy exists between the uncalibrated blackbody surface temperature and the standard temperature. This discrepancy primarily comprises the following components: (1) the blackbody heating and temperature measuring elements are positioned at the back of the blackbody surface, whereas calibration utilizes the front surface, leading to a temperature difference due to the thickness of the radiating surface; (2) the inherent temperature measurement errors of the temperature sensors; and (3) temperature drifts over time in the temperature sensing elements. As the blackbody serves as a standard reference, it is imperative to correct these errors. The measurement accuracy of IR cameras is usually ±2 °C or ±2%, and the greater value is valid (for the most accurate systems, ±1 °C or ±1%, ±5 °C or ±5% for low-end IR cameras) for pyrometers, ±1 °C or ±1% or ±2 °C or ±2% [
19,
20]. The challenge lies in calibrating a blackbody surface source with a precision index of 0.01 K. To achieve this objective, it is essential to clarify three concepts: accuracy, resolution, and display precision. The accuracy of a thermopile infrared sensor by our labrary is 0.1 K, while its resolution and display precision are 0.001 K. This precision refers to the accuracy of temperature measurement at discrete temperature points rather than across a continuous temperature range. For instance, the temperature measurement precision at commonly used blackbody temperatures such as 283 K and 303 K achieves a 0.1 K accuracy. Taking a blackbody standard of 303 K as an example, due to the accuracy limitations of infrared thermometers, different units of the same model may display a precision range from 302.900 K to 303.100 K, all potentially representing the standard 303 K. For a thermopile infrared sensor, functionality is predicated based on the thermoelectric effect, where it converts the received infrared radiation signal into an electrical signal. This is achieved by establishing a relationship between the electrical signal and the temperature value through the voltage difference across the hot and cold junctions (with the cold junction typically being at a standard temperature). This signifies that its deviation at a benchmark temperature of 303 K is a constant value within the ambit of 303 ± 0.1 K. This represents a steady-state error. In other words, for an individual infrared thermometer, the measurement error at the standard 303 K is a constant steady-state error, whereas for multiple infrared thermometers, the error at 303 K falls within a random error range of 303 ± 0.1 K, necessitating experimental verification of each infrared thermometer’s steady-state error at a single temperature point. The correction of steady-state errors is achieved through calibration. An infrared thermometer calibrated to 0.01 K precision corrects the steady-state error of the blackbody surface source, thus achieving temperature control at the 0.01 K level. The calibration method is as follows:
A comparative method was employed for calibration using a standard blackbody radiation source as the reference and a radiation thermometer as the comparator to calibrate the radiation temperature of the blackbody radiation source. The calibration equipment and process are shown in
Figure 1. Firstly, we used a calibrated standard small blackbody to calibrate the thermopile infrared sensor. Then, we used the calibrated thermopile infrared sensor to calibrate the large-area blackbody radiation source. The low-temperature blackbody in the fourth part of the experiment was conducted in a vacuum tank, while the medium-temperature blackbody and high-temperature blackbody were conducted indoors with the blackbody compartment door closed.
The standard and the blackbody radiation source to be calibrated were stabilized at the same temperature. The radiation thermometer was used to measure the radiation temperature display values of both the standard and the blackbody radiation source to be calibrated. The radiation temperature of the blackbody radiation source to be calibrated was calculated using Equation (1):
where
is the radiation temperature of the blackbody radiation source to be calibrated,
is the radiation temperature of the standard blackbody radiation source,
is the radiation thermometer’s measurement value of the standard blackbody radiation source’s radiation temperature,
is the radiation thermometer’s measurement value of the blackbody radiation source to be calibrated, and
is the difference between
and
.
The radiation temperature of the standard blackbody radiation source was calculated using Equation (2):
where
is the spectral radiance of the blackbody, given by Planck’s law [
21,
22], in watts per square meter per steradian per micrometer
,
, and
are the upper and lower limits of the radiation thermometer’s working waveband (μm), respectively;
is the actual temperature measured by the reference thermometer of the standard blackbody radiation source,
is the environmental temperature of the standard blackbody radiation source, and
is the effective emissivity of the standard blackbody radiation source.
2.2. Temperature Test Deviation
The calibration model for the radiation temperature of the blackbody radiation source, the radiation thermometer display value, and the difference between the two can be represented by Equation (3):
In the equation, represents the difference between and .
The relationship between the radiation temperature of the blackbody radiation source to be calibrated, the radiation thermometer display value, and the difference between the two can be represented by Equation (4):
In the equation, represents the difference between and .
The relationship between the radiation temperature of the blackbody radiation source and the thermometer display value is shown in
Figure 2.
During calibration, the actual temperatures of the standard blackbody radiation source and the blackbody radiation source to be calibrated are the same, and the corresponding radiation temperatures of the two blackbody radiation sources are close. It can be assumed that the difference between the radiation thermometer display value and the blackbody radiation source radiation temperature is constant within a small range,
, leading to Equation (5):
Equation (6) can be derived from Equation (5):
The standard blackbody radiation source was aimed at, the position was adjusted, and the measurements were taken. The reference thermometer measurement values and radiation thermometer measurement values of the standard blackbody radiation source were recorded three times.
The blackbody radiation source to be calibrated was aimed at, the position adjusted, and measurements taken. The radiation thermometer measurement values were recorded three times. A total of three sets of comparative measurements were conducted for each calibration temperature point.
During each set of comparative measurements, the standard and the blackbody radiation source to be calibrated should be measured alternately at equal time intervals.
The radiation temperature of the standard blackbody radiation source
and
for each comparative measurement was calculated, using Equation (3). The average values of
and
from multiple comparative measurements were calculated using Equations (7) and (8):
In the formula,
denotes the mean brightness of the standard blackbody radiation source at the average temperature
, and
represents the radiation temperature of the standard blackbody radiation source for the
-th group at the
-th measurement.
where
represents the difference between
and
for the
-th group at the
-th measurement, while
is the average value of
.
The radiation temperature of the blackbody radiation source to be calibrated was calculated using Equation (9):
The temperature deviation of the calibration blackbody was calculated according to Equation (10):
2.3. Uniformity of Temperature Test
The temperature points were selected and evenly distributed within the temperature range of the blackbody radiation source. The uniformity test positions were selected at the middle, upper left, lower left, lower right, and upper right of each channel of the blackbody radiation source. The temperature of the blackbody radiation source being calibrated was set at the test temperature point, with a temperature stability of no more than 0.1 K and 0.1%|t| of the larger one (t is the calibration point temperature value) within 10 min. The position of the radiation thermometer was adjusted to make it coaxial with the center of each channel of the blackbody radiation source; at this time, the radiation thermometer was aimed at the center position of each channel of the blackbody radiation source. A total of three measurements were performed at each position. The temperature uniformity of each channel is the difference between the temperature at each point and the center temperature, calculated according to Equation (11):
In the formula, is the difference between the temperature at each point and the center temperature; is average the measurement of the radiation temperature of the upper, lower, left, and right parts of the blackbody radiation source (i = 1, 2, 3, 4); is the average radiation temperature at the center position of the blackbody radiation source.
The temperature uniformity of the blackbody surface source is the difference between the maximum and minimum values of all temperature measurement points in each channel, calculated according to Equation (12):
In the formula, is the temperature uniformity of the blackbody surface source, is the maximum temperature of all temperature measurement points in each channel, and is the minimum temperature of all temperature measurement points in each channel.
2.4. Auto-Correction System for the Focusing and Motor Control Method
The large-area blackbody temperature auto-correction system primarily consists of a three-coordinate positioning system and an infrared temperature measurement system. The three-coordinate positioning system is composed of a focus adjustment platform, a horizontal movement platform, and a lifting platform. The focus adjustment platform is used to adjust the focus distance of the infrared temperature measurement system, achieving Z-direction distance control. The horizontal movement and lifting platforms were utilized for X–Y plane positioning, enabling the temperature measurement of the same position across different temperature measurement channels. The infrared temperature measurement system comprises an insulation cover, an industrial camera, and two infrared thermometers (thermopile infrared sensors), which are employed to acquire the temperature data on the blackbody surface. The industrial camera captures continuous samples of the focused laser cross spot from the infrared thermometer and uses a focus detection algorithm to determine the optimal focus point, thus identifying the most accurate temperature measurement point for the infrared thermometer. The use of two infrared thermometers first provided timely warnings when the temperature drift of the calibrated dual infrared temperature sensors was too large, in which case the infrared thermometer had to be replaced or recalibrated. Second, in terms of checking the uniformity of the surface source temperature, the main existing method uses an infrared imager, with the NETD of current mid-to-high-end imagers typically at the level of 0.1 K, and the accuracy was roughly ±2 K. However, using calibrated dual infrared thermometers, the temperature uniformity of the surface source at the level of 0.01 K could be roughly estimated.
The flowchart of the focus detection algorithm for the dual infrared thermometers is shown in
Figure 3. Initially, the industrial camera is configured by the PS side, and after configuration, the captured image is processed in the PL part. The image is converted to grayscale, followed by filtering and binarization operations, and finally, the Sobel detection algorithm is applied to the binarized image for edge detection. The largest enclosed image area extracted is then subjected to pixel count detection. After the focusing algorithm, the number of focused laser, and red pixels is counted to determine the most accurate focus point. Once the determination is complete, the infrared thermometer performs temperature detection, and the detected temperature data are sent to the host computer.
The algorithm formula for RGB to the YCbCr color space conversion is as shown in Equation (13):
Since Verilog HDL cannot perform floating-point operations, the formula was converted by scaling up 256 times and then shifting right by 8 bits, (0.083 = 00010101), as shown in Equation (14):
To prevent negative numbers during the calculation process, we further transformed the above formula to obtain Equation (15):
The filtering module is responsible for the noise filtering of image data, eliminating Gaussian noise. Its formula is as follows:
where
is the grayscale value of the pixel point in the original image, and
is the value after Gaussian filtering. The division by 16 in the formula facilitates implementation within the hardware.
The above formula can be structured into a 3 × 3 mask. As shown in
Figure 4, the left side is the original image and the right side is the image output after Gaussian filtering. If Gaussian filtering is applied to the green point in the 56th row and 1st column on the left, the filtered output point will be located in the 57th row and 2nd column (the red point on the right). This means that after Gaussian filtering, the output image will move down one row and one column to the right.
As shown in
Figure 5, the value of the original image at row 0, column 0 is 32 (indicated by the black circle in the figure). If Gaussian filtering is applied to this point, it is found that there are no values on its left and upper boundaries. A solution was proposed: add two rows of zeros on its upper boundary and two columns of zeros on its left boundary to form a 3 × 3 matrix. Gaussian filtering can then be performed using this matrix, and similar processing is applied to other edge points [
23].
The Sobel operator is primarily used for edge detection. The correction environment for large-area blackbody radiation source is usually a closed indoor environment with almost no external interference, so the Sobel algorithm is used to achieve edge detection. Technically, it is a discrete differential operator that computes the approximate value of the gradient of the image brightness function. Applying this operator at any point in the image will produce a corresponding gradient vector or a normal vector [
24].
The Sobel convolution factor consists of two sets of 3 × 3 matrices, one for the horizontal direction and the other for the vertical direction [
25]. Convolution with the image plane yields approximate values of the brightness differences in the horizontal and vertical directions, respectively. If A represents the original image, and Gx and Gy represent the image grayscale values after horizontal and vertical edge detection, respectively, their formulas are as follows:
The grayscale value of each pixel in the image is combined using the following formula to calculate the magnitude of the grayscale at that point:
If the gradient G is greater than a certain threshold, the point (x, y) is considered an edge point.
The optimal focusing strategy for the Z-axis focusing adjustment platform is depicted in
Figure 6. Initially, the Z-axis motor is set to move in a single direction (arbitrary), and the camera mounted on the Z-axis continuously captures the pattern of the cross-laser focus from the infrared thermometer. The image undergoes pixel point collection and state determination based on the procedure outlined in
Figure 3, assessing changes in the number of pixel points: if the count is increasing or remains constant, the motor reverses its direction after a one-second delay following the increase in pixel points; if the count is decreasing, the motor continues its current motion until the pixel points increase, followed by a one-second delay before retreating. The process concludes once the optimal focus position for the motor is ascertained. Upon determining the optimal focus position of the motor, the infrared thermometer acquires the corresponding temperature data and subsequently transmits this information to the host computer.