JPH06317497A - Absorption coefficient measuring method - Google Patents

Abstract

PURPOSE:To enhance accuracy in the measurement by determining a formula of a curve smoothed according to a smoothing spline function based on the measurements of temperature rise and drop of a sample, determining a temperature variation rate by differentiating the formula of the curve, and then calculating an absorption coefficient based on the temperature variation rate. CONSTITUTION:The variation rate of temperature rise and drop of a sample fluctuates significantly due to noise when the sample is irradiated with laser light and the irradiation is eventually interrupted. A formula of a continuous curve is thereby set according to a smoothing spline function. The function is a piecewise polynomial for connecting a set of data points (xi, yi) smoothly. Consequently, the time (t) and the measured temperature T of sample can correspond with variables (x) and (y) to approximate each data point well thus providing a smooth function (curve). The approximate function representative of the temperature variation of sample is then differentiated to determine an absorption coefficient thus obtaining a value more approximate to a real value.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an absorption coefficient measuring method for optical components for high power lasers. High output lasers are YAG lasers, CO lasers, CO lasers.
_It broadly refers to infrared lasers such as ₂ lasers, which have a large output, and visible lasers and ultraviolet lasers, which have a large output. Optical components are used to reflect, collect and diverge the laser light. Since the laser that generates a large output irradiates the optical components with strong light, it is required that the absorption coefficient be low. This is because if the absorption is large, the parts are destroyed by the heat generated by the laser light, and it is not desirable that the power loss of the light is large.

The absorption coefficient is an index showing how the intensity decreases as light travels per unit length inside an optical component. The energy of light is exp (−β
If it is represented by x), this β is called an absorption coefficient. Although it is a phenomenological amount, it is important when evaluating the characteristics of transmissive optical components such as lenses.

[0003]

2. Description of the Related Art As a method of measuring the absorption coefficient of optical parts,
The laser calorimetry method is known. This is a method of irradiating the sample with a light beam while measuring the sample temperature and obtaining the absorption coefficient from the rate of temperature change of the sample over time. Figure 3
1 shows a schematic view of an absorption coefficient measuring device using the Zcalorimeter method. The laser light 1 is incident on the sample 4 and is transmitted or reflected by the sample 4. Some power is absorbed by the sample. The temperature of the sample is measured by the thermocouple 5. The output of the thermocouple is input to the multipoint data acquisition device 2 and processed by the personal computer 3. With such an apparatus, the rate of temperature rise during laser irradiation of the sample (optical component) and the rate of temperature decrease after the irradiation is stopped are determined.

That is, at first, the sample is irradiated with laser light,
Measure the temperature of the sample at regular intervals. From these data, the time derivative of the temperature when the temperature rises (dT / dt) ↑
Can be obtained. Then, the laser light is shut off and the sample is allowed to cool.
The temperature at this time is measured at regular intervals. Then, the time derivative (dT / dt) ↓ of the temperature when the temperature decreases is obtained. From this, the absorption coefficient β is

Β = (2nMC _p ) {(dT / dt) ↑ + (dT / dt) ↓} / LP (n ² +1) (1)

[0006] Here, n is the refractive index of the sample, M is the mass of the sample, C _p is the constant pressure specific heat of the sample, L is the length of the sample, and P is the output of the laser light.

The absorption coefficient β can be obtained based on this equation. Before the equation, the refractive index of the sample, the specific heat, the length,
Mass and the like are known parameters. What must be measured is the change in temperature with time (dT / d
t) ↑ and the temperature change (dT / dt) ↓ when the temperature falls.

A laser is actually applied to measure the temperature of the sample, and data as shown in FIG. 1 is obtained. The graph of temperature change is
It becomes a mountain-shaped graph with rising and falling lines. The horizontal axis represents time and the vertical axis represents temperature. After obtaining such data, the temperature increase ΔT at a small time interval Δt is calculated, and this ratio (ΔT / Δt) is obtained. The fluctuation is large at only one location, so similar calculations are performed at many points. For example, (ΔT / Δt) at 30 to 50 points both when rising and when descending
ask for _j . Here, j is the number of the measurement point on the time coordinate. Then, the average value of these ratios is obtained.

(DT / dt) ↑ = N ⁻¹ Σ _{j = 1} ^N (ΔT / Δt) ↑ _j (2)

(DT / dt) ↓ = H ⁻¹ Σ _{j = N + 1} ^{N + H} (ΔT / Δt) ↓ _j (3)

Here, N and H are the numbers of measurement points when the temperature rises and when the temperature falls. The measurement time is t _j , and the temperature at that time is T _j .

The difference in temperature and time is one time later or two.
Take the difference in time after one. For example, if comparing with the time two later, ΔT and Δt of (ΔT / Δt) are ΔT =
T _{j + 2} −T _j , Δt = t _{j + 2} −t _j . In this way, the derivative at many times is obtained. The method described above is intuitively valid. This is because, starting from actual data, a large amount of data is taken, ratios thereof are calculated, and then an average value is calculated. Data T _j that is the basis of calculation
Is the measured temperature value at time t _j and is the measured value. This value itself is the measured value of the thermocouple and should be correct.

This method should be most reasonable because it is calculated on the basis of real data. It seems intuitively. Many ratios are calculated, but this is done in a computer and does not take much time. Then, the average value of these values is obtained. The same average is taken for both rising and falling. In the case of falling, the differential is negative, so take the absolute value and add these values. This is substituted into (1) to obtain the absorption coefficient. FIG. 2 is a flow chart showing the measured temperature data and the calculation of the absorption coefficient.

[0014]

When measuring the absorption coefficient of an optical component by the laser calorimetry method, it is necessary to find the temperature differential. However, since the problem is a minute temperature change, the measured value is easily affected by noise.

Noise is generated by various causes. The rise of the temperature may not be uniform because the part exposed to the laser light is limited. Sometimes the contact between the thermocouple and the part is poor. In addition, the sample crystal has defects, which may cause non-uniform heat conduction. Furthermore, the impedance of the thermocouple is high, and it may pick up electromagnetic noise. Further, even when the temperature drops after the laser irradiation is stopped, the temperature becomes non-uniform due to the support point of the sample, the state of the surrounding wind, and the like. Therefore, an accurate value cannot be obtained by the method of directly obtaining the rate of temperature change from the actually measured value of temperature. Since the value of the temperature change rate is not accurate, the calculated absorption coefficient is inaccurate.

That is, when the temperature is raised, the temperature should rise uniformly with time, but in reality, there is noise and the electromotive force of the thermocouple often fluctuates. The electromotive force of the thermocouple does not rise uniformly with time. Moreover, the change in electromotive force is not uniform due to noise even when the temperature is lowered. The laser calorimetry method uses not the temperature itself but the change in temperature, but since it is a signal containing noise, the influence of noise becomes stronger when it is differentiated. As a result, the measured value of the time derivative of temperature was inaccurate.

It is an object of the present invention to provide a method of measuring the absorption coefficient of an optical component by the laser calorimetry method with higher accuracy by suppressing the influence of such noise as much as possible.

[0018]

The absorption coefficient measuring method of the present invention comprises irradiating a sample with a light beam and measuring the temperature change of the sample with a temperature sensor to obtain a temperature change rate of the sample due to absorption of the light beam. In the absorption coefficient measuring method for determining the absorption coefficient, a curve formula of the temperature change smoothed by the smoothing spline function is calculated from the measured value, and the temperature change rate is calculated from the curve formula.

[0019]

The change in the sample temperature with time after the sample is irradiated with laser light and the irradiation is stopped is shown in FIG. The cross mark indicates the measured value of the temperature change over time. Since there is noise, the data is scattered. When the temperature rises, the temperature does not rise at a constant and uniform rate, but the rate of increase may be large or small. Even when the laser irradiation is stopped and the temperature drops, the temperature does not drop at a constant rate, but the rate of increase varies. When the absorption coefficient is calculated using the data as it is, an error is generated in no small amount.

Of course, even though the data itself contains noise, the temperature difference and the time difference are obtained from many data, the ratio of these is calculated, and the average value of these is calculated. The influence of noise should be reduced. Moreover, there is an advantage that the data used as the basis of calculation is an actual measurement value. However, it is not accurate because of the large variation in data. The present invention makes this an equation of a continuous curve by a smoothing spline function. The solid line shows the curve smoothed by the method of the invention.

The spline function is the data point (x
_i , y _i ) is a function of piecewise polynomials that smoothly and continuously connects them. This is a function for interpolation, and the continuous equation is a set of higher-order functions. All data points are respected and the function passes through all data points. The number of data points is n, which is (x ₁ , y ₁ ),
It is assumed that they are (x ₂ , y ₂ ), ..., (x _n , y _n ). The spline function f (x) is

It is expressed as f (x) = p _m-1 (x) + Σ _{i = 1} ⁿ c _i (x−x _i ) ^2m-1 ₊ (4). The + sign means that when the value in the parenthesis is negative, it is 0, and when it is positive, it is (x−x _i ) ^2m−1 . This function is a function expressing smoothness and the condition (y _i = f (x _i )) that the data point (x _i , y _i ) is passed.

Σ = ∫ {f ^m (x)} ² dx (5)

It can be obtained from the condition of minimizing
f is the m-th derivative of the function f (x). In JIS, brackets are omitted because they do not fit on the shoulder, but they should not be confused with the mth power. In the case of the natural spline function, the coefficient c _i satisfies the following equation.

Σ _{i = 1} ⁿ c _i x _i ^r = 0 (r = 0, 1, 2, ..., M−1) (6)

[0026] This is a spline function that respects all data points (x _i , y _i ). What is used in the present invention is not this, but the data is approximated by a smooth continuous function that deviates from the data point.
Called the smoothing spline function. In the present invention, since the time t and the temperature T are obtained as data, they are used as variables x and y.
Correspond to. Let the smoothing function be f (x). This is the function that best approximates the group of data points and is the smoothest. Of course, we allow y _i ≠ f (x _i ).
In case of smoothing spline function, instead of (4),

Σ = Σ _{i = 1} ⁿ w _i {f (x) −y _i } ² + g∫ {f ^m (x)} ² dx (7)

Let be the evaluation function. The parameter of the function is determined so that this becomes the minimum. w _i is a weight from 0 to 1
Is a constant of. Since the reliability of data may differ from one another, a high weight is given to highly reliable data. f ^m (x) is the function f as described above.
It is the mth derivative of (x), not the mth power. The previous term of the formula of σ is the same as the evaluation formula of the least squares method when w _i = 1. The latter term is the above-mentioned evaluation formula of the spline function. Simply stated, the above term becomes the minimum when the data is approximated most faithfully as an approximate expression. The latter term is a factor that becomes small in the smooth case. In other words, we are looking for a smooth and highly approximated function. To minimize the value of σ above,
As the function f (x),

F (x) = p _m-1 (x) + Σ _{i = 1} ⁿ c _i (x−x _i ) ^2m-1 ₊ (8)

It is preferable that p _m-1 (x) is a polynomial of degree m-1. The second term is the natural spline function.
The reason for using this as a spline function will be explained shortly.
Since this natural spline function is the spline function itself described above, it is originally a function for interpolation, and may be determined so as to pass through all data points (x _i , y _i ).

However, what is required in the present invention is not to interpolate between all the data points, but to obtain a smooth approximate expression that passes through points distant from the data points. The deviation from the data point is represented by the polynomial p _m-1 (x). Since this is a m-1 polynomial, p _m-1 (x) is not included in the second term in the expression (7) for evaluation. This is because the second term is the square integral of the _m- th order differential expression, and the m-th order differential of p _m-1 (x) is zero. The minimum condition of the second term is determined only by the second term of (8). Then it is clear that this is the minimum if it is a spline function. Therefore, the second term becomes the spline function.

That is, in order to connect the data points having variations with a smooth continuous curve, a smooth function passing through the data points, that is, a spline function is mainly used, and a polynomial that gives a deviation from the data is added to this. You just have to add it. This polynomial is a polynomial of degree m-1 so that it does not enter the equation for evaluating the spline function of degree (2m-1).

P _m-1 (x) = Σ _{i = 0} ^m-1 a _i x ⁱ (9)

To minimize σ in (7),

[0035] _{f (x j) + (-} 1) m g (2m-1)! c _j w _j ^-1 = y _j (10)

Is required to be The method of processing the data as it is without using the spline function is f (x _j )
Since = y _j , only the second term on the left side of the equation (10) is different. Actually, such a natural spline function is not used because it is inconvenient for calculation, and an N spline function based on the difference quotient of the natural spline function is used. this is

F (x) = p _m-1 (x) + Σ _{i = 1} ^nm b _i N _i (x) (11)

N _i (x) = Σ _{j = i} ^{i + m} (x−x _j ) ^2m−1 ₊ / P _ij (x _j ) (12)

P _ij (x _j ) = (x _j −x _i ) (x _j −x _{i + 1} ) ... (x _j −x _j−1 ) (x _j −x _{j + 1} ) ... (x _j − x _{i + m} ) (13)

It is represented by f (x) is 2 in the middle region
It is a polynomial of degree m-1. However, at both ends (x <x ₀ , x
_{In m} <x), it is a polynomial of degree m-1. p _m-1 (x) is also an m-1 polynomial. P _ij (x _j ) is (x _j −x
(x _j −x _j ) of the product from ( _i ) to (x _j −x _{i + m} )
It is the product of m differences excluding. This is the denominator of the function to cut. By comparing the two expressions, it can be seen that the coefficient c _k and the coefficient b _i of the N spline function have the following relationship.

When 1 ≦ k ≦ m c _k = Σ _{i = 1} ^k b _i / P _ik (x _k ) (14)

M + 1 ≦ k ≦ n−m c _k = Σ _{i = km} ^k b _i / P _ik (x _k ) (15)

N−m + 1 ≦ k ≦ n c _k = Σ _{i = km} ^nm b _i / P _ik (x _k ) (16) With this, the above conditional expression is

P _m-1 (x _j ) + Σ _{i = 1} ^nk b _i N _i (x _j ) = y _j j = 1, 2, ..., N (17)

It becomes By solving this, the coefficients b _i , a _k, etc. are obtained, so that the coefficients of the spline function are determined. The spline function minimizes the sum of the squares of the previous term, ie, norm (4). This means minimizing the value of σ. Therefore, this is the smoothest function that can approximate the data value.

The present invention expresses the temperature change of the sample by using a smooth function which can approximate the data. The approximation function is differentiated to obtain the absorption coefficient. The conventional method merely divides the difference in data value by the difference in time to obtain the derivative. This is true to the data value, but the data is noisy and differs from the true value. In reality, the temperature change should occur more smoothly. Therefore, it can be said that the formula of the present invention that can smoothly approximate the data is closer to the true value.

Further, the differential obtained by dividing the data value by the time difference has a large variation, but the differential according to the method of the present invention is a differential of a smooth continuous function, so the variation becomes small. The fact that the standard deviation is small shows its excellence.

[0048]

EXAMPLES The present invention was used to measure the absorption coefficient of ZnSe circular flat plate samples. The absorption coefficient of the lens was measured by irradiating the ZnSe sample with light from a carbon dioxide gas laser and measuring the rate of temperature rise and fall. The absorption coefficient of the same sample was measured 43 times using the conventional method and the method of the present invention, and the standard deviation of the measured values was calculated. The results are shown in Table 1.

[0049]

[Table 1]

The present invention using the smoothed spline function has a standard deviation of about one third. It can be seen that the measurement accuracy is improved by using the method of the present invention.

[0051]

As described above, according to the present invention,
Since the data of the temperature measurement value is not used as it is and is smoothed by the smoothing spline function and the time derivative of the temperature is obtained from this, a minute temperature change can be obtained accurately. Y
Infrared lasers such as AG, CO, and CO ₂ lasers, as well as high-power lasers of various wavelengths (visible light, ultraviolet light) and laser processing machines and laser systems using them. It is extremely effective when used for measuring the absorption coefficient of an optical component used for, for example.

[Brief description of drawings]

FIG. 1 is a graph showing a result of measuring a time change of a sample temperature with a thermocouple when the sample is irradiated with laser light. The horizontal axis represents time and the vertical axis represents temperature. The x mark indicates the measured value. The solid line is smoothed by the smoothing spline function.

FIG. 2 is a flow chart from measurement data of temperature to calculation of absorption coefficient. The left side is the conventional method that calculates the time derivative from the measured temperature value. The right side is the method of the present invention in which the measured value data is smoothed by a smoothing spline function and differentiated to obtain the temperature differential.

FIG. 3 is a schematic view of an absorption coefficient measuring device.

[Explanation of symbols]

 1 Laser light 2 Multi-point data acquisition device 3 Personal computer 4 Sample

Claims (1)

[Claims] 1. An absorption coefficient measuring method for determining an absorption coefficient by irradiating a sample with a light beam and measuring a temperature change of the sample with a temperature sensor to obtain a temperature change rate of the sample accompanying absorption of the light beam. , A curve equation smoothed by a smoothing spline function is obtained from the measured values of rise and fall of the sample temperature, the temperature change rate is obtained by differentiating the curve equation, and the absorption coefficient is calculated from this. Coefficient measurement method.