CN108827915B - Sub-pixel position obtaining method based on photoelectric sensing array for measuring refractive index - Google Patents
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Abstract
The invention discloses a method for obtaining a sub-pixel position based on a photoelectric sensing array to measure refractive index, which belongs to the field of measurement and optics and comprises the following steps: s1 takes m pixels before and after the pixel position corresponding to the critical angle, the total number of the m pixels is (2m +1), the reflectivity corresponding to the (2m +1) pixels is collected to be used as fitting data, S2 adopts a Fresnel reflectivity formula to perform Fresnel reflectivity fitting on the fitting data obtained in the step S1 to obtain a Fresnel fitting function, S3 derives the Fresnel fitting function obtained in the step S2, and the peak point of the derived function is the sub-pixel position corresponding to the critical angle. The invention provides a sub-pixel position obtaining method for measuring a refractive index based on a photoelectric sensing array, which fully utilizes the characteristics of automation and rapidness of an array device in measuring the refractive index and simultaneously improves the precision of refractive index measurement.
Description
Technical Field
The invention belongs to the field of measurement and optics, and particularly relates to a sub-pixel position acquisition method for measuring a refractive index based on a photoelectric sensing array.
Background
The refractive index is an important parameter for reflecting the optical property of a medium, the currently proposed measurement methods are various, and the more representative methods comprise the traditional Abbe refractometer, the optical fiber sensing technology, the refractive index measurement technology of an array device and the Surface Plasmon Resonance (SPR) technology.
Among these techniques, SPR has high measurement accuracy, general optical path anti-interference capability, and high requirements for optical components such as sensitive chips. The Abbe refractometer is based on the critical angle method principle, has higher reliability and higher precision, and is widely applied to various fields of industry, agriculture, national defense, scientific research and the like. However, the method has the defects of needing human eyes to aim at reading, large reading error and low measuring efficiency. Fiber optic sensing techniques have relatively high measurement accuracy, but typically require expensive spectrometers and are environmentally demanding.
The technology for measuring the refractive index by using an array photoelectric semiconductor device (hereinafter referred to as an array device) also utilizes the critical angle method principle, and is a necessary way for the automation of a refractive index measuring device. It utilizes various array devices to detect, such as linear array CCD, area array CCD, linear array CMOS, area array CMOS, photodiode array, etc. The method has the advantages of good reliability, high precision and strong real-time property in measurement performance. Compared with the traditional Abbe refractometer, the measurement efficiency is higher, and the automation of data acquisition, processing, storage and display can be realized. It is worth noting that the key of the technique is to accurately obtain the position of the critical angle, which determines the refractive index measurement accuracy.
At present, the critical angle position is obtained only by the technology of measuring the refractive index by the array device, and the measurement precision is magnitude. The accuracy of a single pixel is limited after all, and in the present day that the manufacturing industry is more and more developed, the accuracy is life. The need for high precision measurements is very urgent!
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a sub-pixel position acquisition method for measuring the refractive index based on a photoelectric sensing array, which fully utilizes the characteristics of automation and rapidness of the array device in measuring the refractive index and simultaneously improves the precision of the refractive index measurement.
The invention discloses a sub-pixel level position extraction method for measuring refractive index based on a photoelectric sensing array. It comprises two processes: firstly, a differential method is adopted to extract the position to be accurate to one pixel, and secondly, sub-pixel position obtaining based on Fresnel reflectivity fitting is adopted.
The differential method comprises the following steps: the photoelectric sensing array detects to obtain light intensity data xi(Ni,Ii) (ii) a Obtaining a reflectance curve r (N)i) (ii) a Obtaining a reflectance differential curve R (N)i) (ii) a Obtaining reflectivity differential curve peak value pixel point information (N)i,Ri). The photoelectric sensing array is used for detecting to obtain light field data, and the light field data is obtained by detecting based on a system device for measuring the refractive index by the photoelectric sensing array. And comparing the data of the detection light field and the data of the background light field to obtain a reflectivity curve, and differentiating the reflectivity values of adjacent pixel positions to obtain a reflectivity differential curve, wherein the position of the peak value of the reflectivity differential curve is the pixel position corresponding to the critical angle. This step is also referred to as differential limit pixel location extraction.
The Fresnel reflectivity fitting sub-pixel method comprises the following steps: scaling by a differential method to obtain a concentration-pixel fitting curve C (N)i) (ii) a The concentration-angle relation curve C (theta) is obtained by angle conversioni) (ii) a Extracting the position of a differential method boundary pixel; collecting a plurality of data points before and after the differential method pixel position; fitting the optical Fresnel reflectivity by using a fitting method; and deriving the fitting formula to obtain the sub-pixel value.
In order to achieve the purpose, the invention provides the following technical scheme:
s1: taking m pixels before and after the pixel position corresponding to the critical angle, wherein the m pixels are (2m +1) pixels in total, collecting the reflectivity corresponding to the (2m +1) pixels as fitting data, wherein m is more than or equal to 3, preferably more than or equal to 100,
s2: and (3) performing Fresnel reflectivity fitting on the fitting data obtained in the step S1 by adopting a Fresnel reflectivity correction formula to obtain a Fresnel fitting function, wherein the adopted Fresnel reflectivity correction formula is as follows:
wherein:
in the formula, riIs the reflectance, θiIs the critical angle, n, corresponding to the ith pixelrFor the real part of the refractive index of the liquid to be measured, niIs the imaginary part of the refractive index of the liquid to be measured, nprismThe refractive index of a triangular prism in the photoelectric sensing array measurement system,
s3: and (4) performing derivation on the Fresnel fitting function obtained in the step (S3), wherein a peak point of the derivation function is a sub-pixel position corresponding to the critical angle.
More specific methods are as follows:
1) detecting by an array device to obtain light intensity data: firstly, an array device refractive index measurement system device is set up to obtain data, and when air background light exists in a sample pool, the array device detects to obtain total reflection background light intensity data
When the liquid to be detected is in the sample pool, the array device detects to obtain the light intensity data x of the detection light fieldi(Ni,Ii)。
2) Obtaining a reflectivity curve: the above-mentioned background light field light intensity and detection light intensity data are pixel label position of array device and correspondent light intensity data, and the detected light field light intensity of same pixel label position is compared with background light field light intensity data so as to obtain reflectivity curve r (N) of reflectivity along with pixel labeli)。
3) Obtaining a reflectivity differential curve: based on the reflectivity curve obtained in step 2), subtracting the reflectivity values of the adjacent pixel label positions to obtain a curve R (N) of the reflectivity differential value along with the pixel labeli)。
4) Obtaining a reflectivity curve differential peak value: the maximum reflectivity differential value corresponding to the pixel label is the pixel position N corresponding to the obtained critical anglei。
5) By the differential algorithm process, the boundary pixel position can be extracted to be accurate to one pixel position.
The next step is to further refine the extraction position to the sub-pixel level by a sub-pixel level acquisition method based on fresnel fitting.
6) And (3) carrying out differential method calibration, specifically, obtaining calibration curves of the refractive indexes of various liquids to be measured relative to critical pixels through the differential method calibration process. The calibration process is to configure a plurality of transparent liquids with different refractive indexes in the refractive index measurement range, and obtain the relationship between the pixels corresponding to the critical angles of the liquids and the refractive indexes of the liquids through the differential algorithm, and the relationship curve is called as a calibration curve. Calibration is a necessary step in the refractive index measurement process.
7) Angle conversion: in order to further obtain the reflectance curve of the reflectance with respect to the incident angle, the reflectance curve of the reflectance with respect to the pixel obtained in step 2 needs to be subjected to coordinate conversion.
The scaling curve obtained in step 6) can be converted into a relation between the array device pixels and the incident angle using the prism refractive index and the liquid refractive index according to the critical angle principle. This curve is called the transfer curve, which is as follows:
finally, converting the critical point pixel into an incidence angle, wherein thetacN represents a refractive index, which is a critical angle of total reflection. n isprismThe refractive index of the prism in the system is measured for the photo-sensing array.
That is, the scaling obtains the relationship between the pixel and the refractive index, and through the conversion process, the correspondence between the pixel and the incident angle can be obtained.
8) Acquiring fitting data: and (3) taking the reflectances corresponding to a plurality of pixels before and after the boundary pixel (the reflectances can be directly obtained through the reflectivity curve obtained in the step (2)) as fitting original data by utilizing the boundary pixel position obtained by the differential method, and then converting the fitting original data into fitting data of the reflectances relative to the incidence angle through angles according to the corresponding relation curve of the pixels and the incidence angle. In practical engineering practice, m pixels before and after the boundary pixel can be taken as a plurality of pixels before and after the boundary pixel, and m is a positive integer.
9) Fresnel reflectivity fitting: and (3) performing curve fitting on the fitting data obtained in the step 8) by adopting an optical reflectivity Fresnel formula to obtain a Fresnel function which is matched with the reflectivity curve and is determined by parameters.
10) Sub-pixel acquisition: and 9) obtaining a derivative of the Fresnel function determined by the parameters obtained in the step 9), wherein the peak point of the derivative function is the sub-pixel position corresponding to the critical angle.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
the invention designs a new method for measuring the sub-pixel position of the refractive index by utilizing the traditional system device for measuring the refractive index by using the array device, thereby greatly improving the measurement precision of the liquid refractive index.
Compared with the characteristics of manual calibration and manual reading of the traditional Abbe refractometer, the traditional array device refractive index measurement system has the advantages of rapidness and automation in measurement because the adopted array device receives light spots and acquires data. However, the technical scheme of the traditional array device refractive index measurement system is still incomplete, the measurement algorithm is not mature, the basic single-pixel precision measurement is realized at most, and if the precision is further improved, a high requirement is required to improve the performance of the array device.
The invention explores the sub-pixel field of the array device, so that the judgment of the boundary of the bright and dark faculae is accurate to the sub-pixel precision, the performance of the array device is fully utilized, and the large-range improvement of the precision is realized.
Drawings
FIG. 1(a) is a flowchart of obtaining a reflectivity differential peak during a Fresnel fitting sub-pixel method for measuring a refractive index based on an array device according to an embodiment of the present invention;
FIG. 1(b) is a flow chart of a Fresnel fitting sub-pixel algorithm based on the refractive index measured by the array device according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of an apparatus for measuring refractive index based on an array device in an embodiment of the present invention;
FIG. 3 is a graph obtained using an array device measurement apparatus for a set of sample liquid detections;
FIG. 4 is a graph obtained by obtaining a reflectivity graph and using a differential method;
FIG. 5 is a plot of the results of a calibration experiment using differential methods;
FIG. 6 is a set of curves of the reflectivity of the liquid to be measured and based on Fresnel fitting.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention discloses a sub-pixel level position extraction method for measuring refractive index based on a photoelectric sensing array. It includes: and two processes, namely, extracting the position to be accurate to one pixel by adopting a differential method, and acquiring the position by adopting a sub-pixel position based on Fresnel reflectivity fitting.
The differential method comprises the following steps: detecting by a photoelectric sensing array to obtain light intensity data; obtaining a reflectivity curve; acquiring a reflectivity differential curve; acquiring a differential peak value; the photoelectric sensing array is used for detecting to obtain light field data, and the light field data is obtained by detecting based on a system device for measuring the refractive index by the photoelectric sensing array. And comparing the data of the detection light field and the data of the background light field to obtain a reflectivity curve, and differentiating the reflectivity values of the positions of adjacent pixels to obtain a differential curve, wherein the differential peak value is the extracted pixel.
The Fresnel reflectivity fitting sub-pixel method comprises the following steps: calibrating by a differential method to obtain a concentration and pixel fitting curve; converting the angle to obtain a concentration-angle relation curve; extracting the position of a differential method boundary pixel; collecting a plurality of data points before and after the differential method pixel position; fitting the optical Fresnel reflectivity by using a fitting method; and deriving the fitting formula to obtain the sub-pixel value.
Specifically, the differential method calibration experiment process comprises the following steps: firstly, a differential method is adopted to complete the extraction of a group of liquid pixel points to be detected, and the method comprises the following processes: detecting by an array device to obtain light intensity data; calculating according to the light intensity data to obtain a reflectivity curve, specifically, comparing the detected light field with the background light field data to obtain the reflectivity curve; calculating according to the obtained reflectivity to obtain a differential curve, specifically differentiating the reflectivity values of adjacent pixel positions to obtain the differential curve; and calculating to obtain a differential peak value according to the differential curve, wherein a pixel point corresponding to the differential peak value is a pixel point needing to be extracted. And then, extracting other four groups of liquid pixel points to be measured by using a differential method to obtain concentration pixel point data of five groups of liquid, and performing linear fitting to obtain a theoretical calibration curve.
The Fresnel fitting sub-pixel position acquisition method comprises the following steps: obtaining a theoretical calibration curve, namely obtaining a concentration pixel curve of the device, and obtaining a concentration-angle relation curve through angle conversion; then, extracting pixel points of the liquid to be detected by a differential method; acquiring information of a plurality of pixels before and after a differential method pixel (for example, information of 250 pixels before and after and 501 pixels in total), wherein the pixel information includes light intensity information and coordinate information; fitting the optical Fresnel reflectivity by using a fitting method to obtain a reflectivity fitting function; and (4) deriving the reflectivity fitting function, wherein the position of the derivative function of 0 is the peak value of the Fresnel fitting formula, and the peak value corresponds to the position of a sub-pixel.
Fig. 1(a) is a flowchart of obtaining a reflectivity differential peak value in the fresnel fitting sub-pixel method process based on the array device to measure the refractive index according to the embodiment of the present invention, and fig. 1(b) is a flowchart of the fresnel fitting sub-pixel algorithm based on the array device to measure the refractive index according to the embodiment of the present invention, and it can be seen from the diagrams that the technical scheme of the present invention mainly includes the following steps:
1) the array device obtains a light intensity curve: firstly, an apparatus system based on array device refractive index measurement is built, and a distribution curve of reflected light is obtained by using the array device. Fig. 2 is a schematic structural diagram of a system device constructed based on an array device for measuring refractive index in the embodiment of the present invention, and as shown in fig. 2, the system device mainly includes a semiconductor laser LD 1, a triangular prism 2, a sample cell 3, an array device 4, and a PC automation control terminal 5. Wherein, the array device detects the air background light in the sample cell to obtain the total reflection background light intensity curve
NiCorresponding to the pixel value size of the ith pixel,
the light intensity value under the air background is detected by the array device when the liquid to be detected is in the sample pool to obtain a light intensity curve x of a detected light fieldi(Ni,Ii). I is 1,2,3 … N, N is the maximum number of pixels of the array device, IiThe corresponding intensity at the ith pixel.
2) Obtaining a reflectivity curve: for the liquid to be detected, the corresponding reflectivity curve can be obtained by utilizing the light intensity of the background light field in the step 1) and the detection light intensity curve corresponding to the liquid to be detected. The data of the light intensity curve of the detection light field and the light intensity curve of the background light field at the same pixel position are divided one by one to obtain the reflectivity curve r of the reflectivity along with the pixel positioni(Ni,ri) Wherein r isiCorresponds to the NthiReflectance value at individual pixel, i.e.
3) Obtaining a reflectivity differential curve: using the reflectivity curve obtained in the step 2) to subtract the reflectivity values of the adjacent pixel positions, thus obtaining a curve R with the reflectivity differential value changing along with the pixel positioni(Ni,Ri) Wherein N isiCorresponding to the size of the pixel value of the ith pixel, RiThe reflectance differential value corresponding to the i-th pixel, i.e. Ri＝ri+1-ri。
4) Obtaining a reflectivity curve differential peak value: using the reflectance differential curve R of 3) aboveiFor curve RiIts peak is sought. The pixel position N corresponding to the peak valueiThat is, the pixel position corresponding to the critical angle of the liquid to be measured at this time is obtained, and a group of concentration pixel data points (C) of the liquid is obtainedi,Ni)。
5) And (3) fitting to obtain a theoretical calibration curve: the process of the differential method completes the extraction of the pixel positions of a group of liquid to be measured. Then, the same method is adopted to complete the extraction of the pixel points of at least four groups of other liquids to be measured. Obtaining at least five (C, N) data points, and performing straight line fitting to obtain a fitting formula as follows:
C＝0.044479×N+(-31.03) (1)
i.e. a calibration curve for the differential method is obtained, where C is the concentration and N is the pixel position.
In actual engineering practice, three data points or six or seven data points can be used for straight line fitting, or any plurality of data points can be used for data fitting.
6) Angle conversion: the differential scaling process obtains a fitting formula (1), the concentration pixel relation in the formula (1) is put into a concentration refractive index formula (2), a relational formula (3) of the refractive index relative to the pixel value is obtained,
n＝0.00185C+1.3331 (2)
n＝8.2286×10-5×N+1.2757 (3)
then, conversion is performed by the total reflectance formula (4):
n＝1.514×sinθc(4)
finally, the conversion of a pixel value and a corresponding angle value is realized, wherein n is the refractive index, and theta iscThe critical angle.
7) Acquiring fitting data: taking a group of liquid to be measured, measuring by using a system device, extracting critical pixel points by using a differential method, taking the reflectivity corresponding to 250 pixels before and after the critical pixel point as fitting data, and totally 501 pixel data points (N)j,rj)，j＝1、2、3、···、500、501。
8) Fresnel reflectivity fitting: for the pixel data point (N) obtained in step 7)j,rj) The pixel values are converted into angles through an angle conversion process to obtain a series of data (theta)i,ri) Then, 501 data points (θ) are corrected by fresnel reflectivity correction equation (4)i,ri) Fitting was performed, and the fitting results are shown in fig. 6.
Wherein:
in the formula, riIs the reflectance, θiIs the critical angle, n, corresponding to the ith pixelrFor the real part of the refractive index of the liquid to be measured, niIs the imaginary part of the refractive index of the liquid to be measured, nprismThe refractive index of a triangular prism in the system is measured for the photoelectric sensing array.
9) Sub-pixel acquisition: and (3) deriving the fitting formula obtained in the step 8) to obtain a curve as shown in a lower graph of fig. 6, wherein the curve has an obvious peak value, the peak value is a critical angle of total reflection of the liquid, the critical angle is known from the previous angle conversion process and corresponds to a critical point pixel value, the critical angle can be converted into a corresponding critical point pixel value by continuing an angle inverse transformation process, and the critical point pixel value is the sub-pixel level position extraction of a group of liquid to be detected.
10) The verification process of the sub-pixel level position extraction algorithm comprises the following steps: through the steps, the scaling process of the differential method is completed, the scaling formula is obtained, and as can be seen from fig. 5, a very ideal fitting effect is achieved, and the scaling formula can be used as a theoretical formula for sub-pixel verification.
And then, performing a calibration experiment on the liquid in a small concentration range by using a Fresnel fitting-based sub-pixel level acquisition method, preparing 8 groups of liquids, and enabling the boundary pixel change corresponding to the change of the concentration gradient of the liquids to be at a sub-pixel level, and finally realizing sub-pixel measurement by using the algorithm disclosed by the invention to obtain a sub-pixel calibration formula (6).
C＝0.044479×N+(-31.03) (5)
C＝0.045×N+(-31.57) (6)
Wherein, N is the pixel value of the array device, and C is the concentration value. The slope of the fitting formula corresponds to the resolution of the device, from the fitting formula of the slope and the resolution of the device, the resolution of the device obtained by the differential method is 0.044479, the intercept is-31.03, the resolution of the device obtained by the sub-pixel method is 0.045, and the intercept is-31.57, and from the comparison of the fitting formulas, the fitting formulas are very close to each other, and as can be seen from fig. 5, in the process of completing a calibration experiment by the differential method, the fitting effect is very ideal and can be used as a theoretical comparison formula to verify the sub-pixel algorithm. The sub-pixel algorithm is used for carrying out a calibration experiment in a low concentration gradient range, the boundary pixel position corresponding to the concentration gradient change range is in a sub-pixel level, the calibration experiment is completed, and compared with a differential method calibration theoretical curve result, the calibration experiment is very close, so that the sub-pixel algorithm is verified to achieve a relatively ideal effect, and the precision is further improved.
The design process of the method is specific to the linear array sensor in the array device, and for the area array sensor, the conversion process from two dimensions to one dimension is realized only by replacing the light intensity curve received in the linear array sensor with light intensity two-dimensional plane distribution data and then linearly superposing the light intensity curve in the longitudinal direction.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (4)
1. A sub-pixel position obtaining method for measuring refractive index based on a photoelectric sensing array is characterized by comprising the following steps:
s1: detecting by a photoelectric sensing array device to obtain light intensity data, calculating according to the light intensity data to obtain a reflectivity curve, calculating according to the reflectivity curve to obtain pixels corresponding to a critical angle, taking m pixels before and after the pixel position corresponding to the critical angle, wherein the m pixels are (2m +1) pixels in total, collecting the reflectivity corresponding to the (2m +1) pixels to serve as fitting data, wherein m is more than or equal to 3,
s2: and (3) performing Fresnel reflectivity fitting on the fitting data acquired in the step S1 by using a Fresnel reflectivity correction formula to obtain a Fresnel fitting function, wherein the Fresnel reflectivity correction formula is as follows:
wherein:
in the formula, riIs the reflectance, θiIs the critical angle, n, corresponding to the ith pixelrFor the real part of the refractive index of the liquid to be measured, niIs the imaginary part of the refractive index of the liquid to be measured, nprismMeasuring the refractive index of a triangular prism in the system for the photoelectric sensing array;
s3: and (4) performing derivation on the Fresnel fitting function obtained in the step (S2), wherein a peak point of the derivation function is a sub-pixel position corresponding to the critical angle.
2. The method for obtaining the sub-pixel position based on the refractive index measurement of the photoelectric sensing array as claimed in claim 1, wherein the reflectivity curve obtaining method comprises: and comparing the light intensity of the detection light field with the same pixel label with the light intensity data of the air background light field to obtain a reflectivity curve of the reflectivity along with the position of the pixel label.
3. The method as claimed in claim 2, wherein a reflectivity curve is obtained by calculation according to the light intensity data, a differential curve is obtained by calculation according to the obtained reflectivity, specifically, a differential curve is obtained by differentiating the reflectivity values of adjacent pixel positions, a differential peak value is obtained by calculation according to the differential curve, and the pixel corresponding to the differential peak value is the pixel to be extracted.
4. The method as claimed in claim 3, wherein in step S2, the reflectivity corresponding to a plurality of pixels before and after the pixel position corresponding to the critical angle is taken as the fitting raw data, and then the fitting raw data is converted into the fitting data of the reflectivity relative to the incident angle through angle according to the corresponding relation curve of the pixel and the incident angle,
specifically, firstly, a plurality of fitting curves of the concentration of the liquid to be measured with respect to the critical point pixels are obtained, the fitting curves are calibration curves, a detection curve of the reflectivity with respect to the critical angle is obtained through the conversion process of the critical point pixels and the critical angle,
wherein, the conversion process converts the critical point pixel into the incidence angle by the following total reflectivity formula by using a calibration curve,
wherein, thetacIs the critical angle of total reflection, n represents the refractive index, nprismThe refractive index of the prism in the system is measured for the photo-sensing array.
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