TWI857141B - Linear correction method for optical measuring device, optical measuring method and optical measuring device - Google Patents

Abstract

High-precision linear correction of an optical measuring device using a CMOS linear image sensor. A linear correction method for an optical measuring device having a CMOS linear image sensor is provided, comprising the following steps: an exposure step, changing the exposure time so that a reference light of a constant intensity is sequentially incident on a photosensitive element of interest of the CMOS linear image sensor; a measurement value acquisition step, sequentially acquiring the measurement value of the photosensitive element of interest; an actual linear error calculation step, sequentially calculating an actual linear error indicating the difference between a linear value obtained based on the exposure time corresponding to the measurement value and the measurement value; and a fitting step, for each of the actual linear errors, performing fitting of a first function indicating a first linear error.

Description

Linear correction method for optical measuring device, optical measuring method and optical measuring device

The present invention relates to a linear correction method for an optical measuring device, an optical measuring method and an optical measuring device.

CCD (Charged-coupled devices) linear image sensors can be used in optical measurement equipment (such as multi-channel spectrometers, etc.). The specific wavelength portion of the measurement light dispersed by the diffraction grating is incident on each photosensitive element configured in the CCD linear image sensor, and an electrical signal corresponding to the light intensity is output from these photosensitive elements. However, although CCD linear image sensors generally have the advantage of high sensitivity, their structure tends to be complex and expensive.

[Patent Literature]

[Patent Document 1] Patent Publication No. 5-15628

CMOS (Complementary Metal Oxide Semiconductor) linear image sensors are also known as electronic components with the same functions as CCD linear image sensors. CMOS linear image sensors have the advantages of extremely simple structure, low cost, low power consumption, and easy speed increase.

However, the CMOS linear image sensor has a disadvantage that its linearity is lower than that of the CCD linear image sensor. That is, there is a disadvantage that even if light with an intensity of α times is incident on each photosensitive element configured in the CMOS linear image sensor, a measurement value of α times may not be obtained. Therefore, there is a problem that the intensity of the measured light cannot be immediately determined based on the original output value of the CMOS linear image sensor. Therefore, when the CMOS linear image sensor is used as an optical measurement device, high-precision linear correction is required.

The present invention is made in view of the above-mentioned problems, and its purpose is to provide a linear correction method capable of performing linear correction on an optical measuring device using a CMOS linear image sensor with high precision, an optical measuring method using the method, and an optical measuring device.

In order to solve the above problems, the linearity correction method according to the present invention is a linearity correction method for an optical measuring device, which is characterized by having a CMOS linear image sensor, and includes the following steps: an exposure step, changing the exposure time so that the reference light of constant intensity is incident on the focus light receiving element of the CMOS linear image sensor in sequence; a measurement value acquisition step, sequentially obtaining the measurement value of the focus light receiving element; an actual linear error calculation step, sequentially calculating the actual linear error indicating the difference between the linear value obtained based on the exposure time corresponding to the measurement value and the measurement value; and a fitting step, for each of the actual linear errors, performing fitting of a first function indicating a first linear error.

Here, the first function may be a quadratic function.

In addition, the fitting step may determine the variable parameter of the first function by least squares using a target function indicating the total amount of the difference between each of the actual linear errors and the first linear error. The target function may include a term indicating the difference between the first linear error and the actual linear error corresponding to each of the measured values. Such terms may be weighted by a deviation amount indicating the deviation of each of the measured values.

In addition, the method may further include an exposure time correction step of performing exposure time correction on the measurement value corrected by the first function.

In addition, the exposure time correction step can be performed by applying a second function that approaches a predetermined value as the exposure time becomes longer to the measured value corrected by the first function to perform the exposure time correction.

Here, the second function can be a fractional function.

In addition, the measurement value can be obtained based on the difference between the first output value of the focus light receiving element when the reference light is incident and the second output value of the focus light receiving element when the reference light is not incident.

Furthermore, the fitting step may utilize the measured value obtained based on the first output value above a predetermined threshold to perform the fitting.

In addition, the CMOS linear image sensor may include an unfocused light-receiving element, and no light is incident on the unfocused light-receiving element during the time when the reference light is incident on the focused light-receiving element. At this time, the linear correction method may further include a basic correction value calculation step, which is to calculate a basic correction value that makes the measurement value of the unfocused light-receiving element close to zero when the reference light is incident on the focused light-receiving element. The measurement value acquisition step may sequentially obtain the measurement value corrected by the basic correction value.

According to the optical measurement method of the present invention, a linear correction method of an optical measurement device described in any of the above items is used. When the measurement light is incident on the focus light-receiving element, the measurement value of the focus light-receiving element is corrected based on the first function.

There are a plurality of the light-receiving elements of interest. In addition, when the measurement light is incident on each of the light-receiving elements of interest, the measurement value of the light-receiving element of interest can be corrected based on a function representing the first function obtainable for each of the plurality of light-receiving elements of interest.

The optical measuring device according to the present invention comprises: a memory device for storing the correction parameter corresponding to the first function obtained by any of the linear correction methods described above; and a correction device for correcting the measurement value of the concerned light-receiving element using the correction parameter when the measurement light is incident on the concerned light-receiving element.

10: Optical measurement device

11: Light source (sample)

12: Gap

13: Cut-off filter

14: Collimator

15: Diffused grating

16: Focusing lens

17:CMOS linear image sensor

17-i (i=0~1023): light receiving element

18: Computing Department

FIG1 shows the overall structure of an optical measuring device according to one embodiment of the present invention.

Figure 2 shows a schematic diagram of a CMOS linear image sensor.

FIG3 shows a flow chart of the method for calculating the correction parameters.

FIG4 shows a flow chart of the method for calculating the correction parameters.

Figure 5 shows the spectrum of the measured value Si.

Figure 6 shows a partial enlarged view of Figure 5.

Figure 7 shows the variation of the measured value Si' after the first correction with respect to the increase of the exposure time t compared to the ideal straight line Li.

Figure 8 shows the relationship between the measured value Si' after the first correction and the actual linear error ei'.

Figure 9 shows the fitting plot of the function f(Si') to the actual linear error ei'.

Figure 10 shows the relationship between the second corrected measurement value Si" and the actual linear error ei" using the function f.

Figure 11 shows the variation of the actual linear error ei" with increasing exposure time t.

Figure 12 shows the relationship between the third corrected measurement value Si''' and the actual linear error ei''''.

FIG13 shows a flow chart of the optical measurement method using correction parameters.

Below, the embodiments of the present invention will be described in detail with reference to the attached drawings.

FIG1 shows a structural diagram of an optical measuring device according to one embodiment of the present invention. The optical measuring device 10 measures the light intensity of each wavelength, that is, the spectrum, by dispersing light emitted from a sample such as a light source 11. The spectrum can be directly used as optical property information of the light source 11, for example. In addition, when the sample is a thin film, the spectrum of the reflected light from the thin film can be used, for example, to calculate the thickness of the thin film.

Light emitted from a sample, such as a light source 11, is applied to a slit 12 provided in an optical measuring device 10. The slit 12 has, for example, a long and narrow rectangular opening. A cutoff filter 13 is provided on the back of the slit 12 as required. The cutoff filter 13 blocks light with a wavelength outside the measuring range. The measuring light that has passed through the cutoff filter 13 reaches the collimator 14. The collimator 14 is, for example, a concave mirror with a constant curvature, which reflects the measuring light passing through the slit 12 and converts it into parallel light, and irradiates the parallel light to the diffraction grating 15.

The diffraction grating 15 diffracts each wavelength component of the light emitted from the collimator 14 in a direction corresponding to the wavelength. The diffraction grating 15 is, for example, a reflective diffraction grating, and a plurality of grooves may be provided on the reflective surface, the plurality of grooves extending in the same direction as the opening of the slit 12. As a result, the diffraction grating 15 reflects each wavelength component of the light emitted from the collimator 14 so that its intensity increases in the direction corresponding to the wavelength.

The focusing lens 16, for example, a concave mirror having a constant curvature, reflects the light of each wavelength component diverted by the diffraction grating 15, and focuses it on each light receiving element arranged in the CCD linear image sensor 17. As schematically shown in FIG2, the CCD linear image sensor 17 includes a plurality of (here, 1024) light receiving elements 17-0 to 17-1023, which are arranged at equal intervals in the diffraction direction of the diffraction grating 15. Each light receiving element 17-i includes a photodiode, which stores a charge that increases with the intensity and time of the received light, and outputs a value corresponding to the amount of charge stored. Each light receiving element 17-i is assigned a wavelength according to its configuration order, and outputs the intensity of the optical component assigned the wavelength. Herein, the subscript i represents the wavelength channel (0~1023).

The output value of each light receiving element 17-i is input to the calculation unit 18 mainly composed of a computer. The calculation unit 18 applies various corrections such as linear correction to each output value to obtain the measured value of the light intensity of each wavelength component.

The CMOS linear image sensor 17 has the disadvantage of poor linearity as described above. Therefore, in the optical measuring device 10, various corrections are made to the raw output values of the light receiving elements 17-i of the CMOS linear image sensor 17 to achieve linearity. That is, conversion based on correction parameters is applied to the raw output value of each light receiving element 17-i and used as a measurement value. The measurement value thus obtained has so-called linearity, and when the light intensity increases by α times, it also increases by α times.

FIG3 and FIG4 show a flow chart of a method for calculating linear correction parameters. Here, the correction of the measured value performed by the CMOS linear image sensor 17 includes the following three corrections: 1) a first correction to prevent the measured value from becoming less than zero in the short wavelength region; 2) a second correction to achieve linearity in the region with high light intensity; 3) a third correction to achieve linearity in the region with low light intensity. These three corrections are applied sequentially to the original output value of each light receiving element 17-i. The processing shown in FIG3 and FIG4 is executed by a computer such as the calculation unit 18.

In order to obtain the correction parameters for the first correction, the second correction and the third correction, first, in the optical measuring device 10, each light receiving element 17 of the CMOS linear image sensor 17 is in a state where no light is incident from the slit 12 into the device, and the original output value Ai0 of each light receiving element 17-i of the CMOS linear image sensor 17 is obtained (S101).

Next, reference light with a constant light intensity, such as white light from a halogen lamp, is incident from the slit 12 into the interior of the device, and while increasing the exposure time t from 0 to tmax, the original output value Ai of each light receiving element 17-i of the CMOS linear image sensor 17 is obtained (S102). When the exposure time t changes from ts to ts to tmax, the output value Ai of each wavelength channel i contains a tmax/ts value (here tmax=10000).

Next, the measurement value Si is calculated, which is the value obtained by subtracting the output value Ai0 from the output value Ai (S103). When the exposure time t changes from ts to ts to tmax, the measurement value Si of each wavelength channel i includes the tmax/ts value.

FIG5 is a spectrum diagram showing the measured value Si. The horizontal axis corresponds to the wavelength channel i, and the vertical axis corresponds to the measured value Si. Here, four spectra corresponding to exposure times t=100, 3000, 6000, and 10000 are shown. As shown in the figure, the measured value Si increases from near zero near the wavelength channel i=200, and decreases to near zero near the wavelength channel i=600. FIG6 is an enlarged view showing the portion of the wavelength channel i=0~150 in FIG5. As shown in FIG6, in the region where the wavelength channel i is small (i.e., short wavelength), the measured value Si can be less than zero. Therefore, here, for each exposure time t, the average value of the measurement value Si is calculated for a predetermined number of wavelength channels i (here i=0 to 9), wherein the measurement value Si is initially regarded as zero and the value is set to b (S104). That is, when the exposure time t changes from ts to ts to tmax, the correction parameter b (basic correction value) includes the value tmax/t. The first corrected measurement value Si' is obtained by subtracting the correction parameter b from the measurement value Si for each combination of exposure time t and wavelength channel i (S105). In addition, as described later, here, in order to obtain the statistical variation of the first corrected measurement value Si', the processing of S102 to S105 is repeated several times (for example, 100 times) under the same conditions.

Next, the measurement value Si' is converted into an actual linear error ei'. FIG. 7 is a graph showing the change of the first corrected measurement value Si' relative to the increase of the exposure time t compared to the ideal straight line Li. In the graph, a plane having a horizontal axis indicating the exposure time t and a vertical axis indicating the first corrected measurement value Si' is shown. The ideal straight line Li is a straight line connecting the point (tmax, Si'max) formed by the maximum exposure time t=tmax and the value of the first corrected measurement value Si' at that time (this value is called Si' max) and the origin (0,0) (S106). The actual linear error ei', as shown in the following mathematical formula (1), shows the ratio of the difference between the ideal straight line Li and the first corrected measurement value Si' to the first corrected measurement value Si'.

FIG8 is a graph showing the relationship between the first correction output value Si' and the actual linear error ei'. Here, the case of i=456 is taken as an example. As shown in the figure, as the output value Si' after the first correction increases, the actual linear error ei' decreases. In addition, in the area where the measured value Si' after the first correction is small, the actual linear error ei' fluctuates greatly, while in the area where the measured value Si' after the first correction is large, the actual linear error ei' fluctuates very little. Therefore, in the second correction, the linearity of the measured value of the CMOS linear image sensor 17 is improved mainly in the area where the measured value Si' after the first correction is large, that is, the value of the exposure time t falls in a large area.

Therefore, first, the error △ei' of the actual linear error ei' is calculated using the following mathematical formula (2) (S108). Mathematical formula (2) is derived from the well-known law of propagation of error. The error △ei' is calculated for each combination of exposure time t and first corrected measurement value Si'. In mathematical formula (2), △Si' and △Si'max are sample standard deviations representing the first corrected measurement values Si' and Si'max. As shown in FIG8, when the values of exposure time t and first corrected measurement value Si' are smaller, the error △ei' increases, and when the values are larger, the error △ei' decreases. The error △ei' is an example of a variation indicating a variation of the measurement value Si', and the variation can be obtained by another calculation formula.

Next, each wavelength channel i is provided with a quadratic function f(Si')=C2×Si'2+C1×Si'+C0 for displaying a linear error, and in each wavelength channel i, f(Si') is fitted to the actual linear error ei' (S109). The least squares method is used for fitting. As a result, coefficients C0, C1, and C2 are determined. Here, a quadratic function is used as an example of the first function of the present invention, but it goes without saying that it can be another function.

Furthermore, the fitting in S109 can be performed only for the wavelength channel i whose output value Ai at the exposure time t=tmax is above the predetermined threshold. In this case, the coefficients C0, C1 and C2 will be determined only for this wavelength channel i.

Figure 9 is a graph showing the fit of the quadratic function f(Si') and the actual linear error ei'. Again, take the case of i=456 as an example. The horizontal axis represents the measured value Si', and the vertical axis represents the actual linear error ei'. The black dots in the figure represent the measurement points (Si', ei') consisting of the measured value Si' and the actual linear error ei'. The curve sloping downward to the right shows the shape of the quadratic function f that fits these measurement points. In addition, the vertical line segment passing through each black dot indicates the error △ei'. As shown in the figure, in the area where the measured value Si' is small (that is, the area where the exposure time t is shorter), the error △ei' is relatively large. Then, in the region where the error △ei' is large as described above, the degree to which the quadratic function f fits the measurement point is reduced, and conversely, in the region where the error △ei' is small, the degree to which the quadratic function f fits the measurement point is increased. Therefore, the target function in the least squares method is the weighted sum of the differences between the quadratic function f(Si') and the actual linear error ei', and the inverse of the error △ei' is used as the weight. As a result, in the region where the exposure time t and the value of the first corrected measured value Si' are large, the quadratic function f(Si') is fitted by the actual linear error ei'.

Next, using the coefficients C0, C1 and C2 determined in S109, the second corrected measurement value Si" (S110) is calculated using the following mathematical formula (3).

In addition, in S109, coefficients C0, C1, and C2 are determined for each wavelength channel i. Therefore, when calculating the second corrected measurement value Si", the coefficients C0, C1, and C2 determined for the same wavelength channel i are used.

For simplicity, the average values (representative values) of C0, C1 and C2 are calculated, and in mathematical formula (3), these representative values (i.e., a quadratic function represents a plurality of quadratic functions for each wavelength channel) can be used in common in all wavelength channels i. In particular, when S109 fitting is performed only for wavelength channels whose first corrected measurement value Si' at exposure time t=tmax is above a predetermined threshold, for wavelength channels that have not yet been fitted by S109, the average values of C0, C1 and C2 can be used to properly calculate the second corrected measurement value Si".

Next, for each wavelength channel i, the second corrected measurement value Si" is converted into the actual linear error ei" (S111). The actual linear error ei" can also be calculated by the same equation as the above mathematical formula (1).

FIG10 shows a relationship diagram between the second corrected measurement value Si" using the function f and the actual linear error ei". Again, take the case of i=456 as an example. As shown in the figure, the actual linear error ei" is a sufficiently small value in the region where the measurement value Si" is above 0.2, and linearity can be fully achieved in this region. However, in the region where the measurement value Si" is less than 0.2, that is, in the region where the exposure time is short, the linearity is insufficient. Therefore, in this embodiment, exposure time correction is performed as the third correction. The exposure time correction is to increase the correction of the measurement value Si" in the region of short exposure time according to the short exposure time. Specifically, the third corrected measurement value Si''' is defined by the following mathematical formula (4). That is, the third corrected measurement value Si''' is obtained by multiplying the second corrected measurement value Si" by the fractional function t/(dt) as an example of the second function of the present invention. Here, d is the corrected exposure time. The larger d is, the larger the correction amount is. However, in the area where the exposure time t is large, the correction amount will become smaller, and the difference between the second corrected measurement value Si" and the third corrected measurement value Si''' becomes smaller. In addition, the second function is not limited to the above-mentioned fractional function, and is a function that approaches a predetermined value (here 1) as the exposure time t increases and increases as the exposure time approaches 0. Any function can be used as long as the shape is changed using a variable parameter.

Next, as shown in the following mathematical formula (5), it is assumed that the third corrected measurement value Si''' is proportional to the exposure time t.

Using mathematical formulas (4) and (5), the actual linear error ei" corresponding to the second corrected measurement value Si" is shown in the following mathematical formula (6), which is expressed as a function g(t) of the exposure time t with the correction parameter d.

Next, using the result of S111, the function g(t) is fitted to the measurement point (t, ei") (S112). As a result, the correction parameter d is determined. FIG11 is a graph showing the fitting. Again, the case of i=456 is taken as an example.

Then, the second corrected measurement value Si" is converted into the third corrected measurement value Si''' using the determined parameter d and mathematical formula (4) (S113). In addition, the correction parameter d is determined for each wavelength channel i in S112. Therefore, for each wavelength channel i, the correction parameter d corresponding to the wavelength channel i can be used and the third corrected measurement value Si''' can be calculated using mathematical formula (4). Alternatively, the average value of the correction parameter d can be calculated, and the average value can be shared for all wavelength channels i, and the third corrected measurement value Si''' can be calculated using mathematical formula (4).

Figure 12 is a graph showing the relationship between the third corrected measurement value Si''' and the actual linear error ei''' calculated based on the third corrected measurement value Si'''. Similarly, take the case of i=456 as an example. As shown in the figure, through the first to third corrections, the linear error ei''' is within a sufficiently small value in the entire range of Si''', so it can be seen that sufficient linearity is achieved in all areas.

Finally, each wavelength channel Ai0 obtained in S101, the correction parameters C0, C1 and C2 obtained in S109, and the correction parameter d obtained in S112 are stored in a memory or the like (S114). These correction parameters are used for optical measurement of the sample.

FIG13 is a flowchart for performing optical measurement using the correction parameters saved as described above. First, light emitted from a sample such as a light source 11 is irradiated to the slit 12, and the output value Ai (i=0~1023) of the CMOS linear image sensor 17 is obtained by the calculation unit 18 (S201). The exposure time ta of the measurement light to the CMOS linear image sensor 17 at this time can be set, and ta can be a value below the above tmax, and can be set to a sufficiently large value.

Next, the calculation unit 18 obtains the measurement value Si (i=0~1023) by subtracting the correction parameter Ai0 from the Ai obtained in S201 (S202). In addition, the average value of the measurement value Si is calculated for the wavelength channel i=0~9 and is set to b (S203). Then, the first corrected measurement value Si' is obtained by subtracting the correction parameter b from the measurement value Si (S204).

The calculation unit 18 also applies the above mathematical formula (3) to the first corrected measurement value Si' and obtains the second corrected measurement value Si" (i=0~1023) (S205). At this time, as the correction parameters C0, C1 and C2, the correction parameters corresponding to the same wavelength channel i are used, and they can be stored for each wavelength channel i. If a common value (average value) is stored for all wavelength channels, this value is used.

The calculation unit 18 uses the exposure time ta and the correction parameter d, and calculates the third corrected measured value Si''' from the second corrected measured value Si" by the above mathematical formula (4) (S206). Here, as the correction parameter d, if the correction parameter is saved for each wavelength channel i, the correction parameter corresponding to the same wavelength channel i is used. If a common value (average value) is stored for all wavelength channels, this value is used.

Afterwards, the calculation unit 18 displays the third corrected measurement value Si''' calculated in S205 (S207), and outputs it by printing or communication (S207). When the sample is a thin film, the calculation unit 18 can use the second corrected measurement value Si" calculated in S206 to calculate the film thickness. The film thickness can be calculated using a known algorithm.

According to the linear correction method of the optical measuring device 10 described above, by performing the first to third corrections on the output value Si of the CMOS linear image sensor 17, a measurement value Si''' with sufficient linearity can be obtained and a high-precision spectrum can be obtained. In addition, using this spectrum, the film thickness of the sample, etc. can be calculated with high precision.

The present invention is not limited to the above-mentioned embodiments, and various modifications can be made. Of course, such modifications are also included in the scope of the present invention.

Claims (11)

A linearity correction method is provided, which has a CMOS linear image sensor and is used in an optical measuring device, and is characterized by comprising the following steps: an exposure step, in which the exposure time is changed, and a reference light of a constant intensity is sequentially incident on a photosensitive element of interest of the CMOS linear image sensor; a measurement value obtaining step, in which the measurement value of the photosensitive element of interest is sequentially obtained; an actual linearity error calculation step, in which the actual linearity error indicating the difference between the linearity value obtained based on the exposure time corresponding to the measurement value and the measurement value is sequentially calculated; and a fitting step. ing) step, for each of the actual linear errors, performing fitting of a first function indicating a first linear error, wherein the fitting step is to determine a variable parameter of the first function using a least square method of a target function indicating the total amount of the difference between each of the actual linear errors and the first linear error, the first function being a quadratic function, the target function including terms indicating the difference between the first linear error and the actual linear error corresponding to each of the measured values, and these terms are weighted by a deviation amount indicating the deviation of each of the measured values. A linearity correction method for a CMOS linear image sensor as claimed in claim 1, wherein the first function is a quadratic function. The linear correction method of claim 1 further comprises an exposure time correction step of performing exposure time correction on the measurement value corrected by the first function. As in claim 3, the linear correction method, wherein the exposure time correction step is to apply a second function that approaches a predetermined value as the exposure time becomes longer to the measured value corrected by the first function to perform the exposure time correction. A linear correction method as claimed in claim 4, wherein the second function is a fractional function. The linear calibration method of claim 1 or 2, wherein the measurement value is obtained based on the difference between the first output value of the photosensitive element of interest when the reference light is incident and the second output value of the photosensitive element of interest when the reference light is not incident. The linearity correction method of claim 6 is characterized in that it is a linearity correction method for a CMOS linear image sensor, wherein the fitting step is performed using the measurement value obtained based on the first output value above a predetermined threshold. The linear correction method of claim 1 or 2, wherein the CMOS linear image sensor includes a non-focus light-receiving element, and no light is incident on the non-focus light-receiving element during the time when the reference light is incident on the focus light-receiving element; the linear correction method further includes a basic correction value calculation step, which is to calculate a basic correction value that makes the measurement value of the non-focus light-receiving element close to zero when the reference light is incident on the focus light-receiving element; the measurement value acquisition step is to sequentially obtain the measurement value corrected by the basic correction value. An optical measurement method uses the linear correction method of any one of claim items 1 to 8, and when the measurement light is incident on the focus light-receiving element, the measurement value of the focus light-receiving element is corrected based on the first function. As in claim 9, the optical measurement method, wherein: there are a plurality of the photosensitive elements of interest, and when the measurement light is incident on each of the photosensitive elements of interest, the measurement value of the photosensitive element of interest is corrected based on a function representing the first function obtainable for each of the plurality of photosensitive elements of interest. An optical measuring device, characterized by comprising: a memory device for storing a correction parameter corresponding to the first function obtained by the linear correction method of any one of the request items 1 to 8; and a correction device for correcting the measurement value of the concerned light-receiving element using the correction parameter when the measurement light is incident on the concerned light-receiving element.