Pupil diameter measurement method and device based on real-time calibration
Patent Information
- Application Number
- CN202511188524.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-25
- Publication Date
- 2026-09-08
- Estimated Expiration
- 2045-08-25
AI Technical Summary
例如,临床环境中需快速测量(如脑卒中评估),但患者头部移动难以控制
[0036] 1) Significantly improve measurement accuracy: By dynamically and in real time marking the ratio between pixels and physical size during each measurement, the system error introduced by the slight changes in the relative distance and angle between the camera and the human eye is effectively eliminated, greatly improving the accuracy of pupil diameter measurement.
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Figure CN121080898B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of pupil diameter measurement technology, and in particular to a pupil diameter measurement method and apparatus based on real-time calibration. Background Technology
[0002] The application of pupil diameter measurement is wide-ranging, primarily driven by the multifunctionality of the pupil as a physiological indicator. In neuroscience and psychology, pupil diameter dilates with increasing cognitive task difficulty (e.g., mental arithmetic, decision-making tasks) during cognitive load assessment, used to study attention, memory, and emotional processing. In emotional response research, pupil changes in response to positive / negative stimuli (e.g., images, music) reflect emotional arousal. This application requires non-invasive, real-time monitoring methods to quantify psychological states, aiding in diagnosis or experimental design. In human-computer interaction and engineering, improving safety and user experience requires real-time, high-precision physiological feedback technology. For driver / pilot fatigue monitoring, pupil dilation is correlated with fatigue levels, used in early warning systems. In virtual reality (VR), pupil changes can be used to adjust interface brightness or content, reducing dizziness. In advertising effectiveness testing, pupil dilation reflects consumer interest in advertising (neuromarketing). In drug research and toxicology, rapid, non-invasive drug response indicators are needed to support pharmacodynamics or forensic identification. In drug effect assessment scenarios, opioids (such as morphine) cause pupil constriction, while stimulants (such as cocaine) cause pupil dilation. Pupil changes are used in drug rehabilitation monitoring to assess withdrawal symptoms or relapse.
[0003] As a "physiological window," the measurement of pupil diameter essentially aims to transform complex neurological, psychological, or pathological states into quantifiable, objective data, serving medical applications, security monitoring, business optimization, and scientific research. Advances in pupil diameter detection technology (such as wearable eye trackers) are driving the continuous expansion of its applications.
[0004] Existing pupil measurement technologies, especially camera-based pupil meters, primarily estimate pupil diameter through image analysis. Their core processes and technical characteristics are as follows: Image acquisition: A camera captures images of the eye (typically using near-infrared illumination to enhance the contrast between the iris and pupil); Image processing: The pupil outline is located using edge detection (e.g., Hough transform, threshold segmentation) or machine learning models; Calibration and scaling: The ratio of pixels in the image to actual physical dimensions (e.g., millimeters) is pre-determined using a reference object of known size (e.g., a calibration rod), converting the number of pixels occupied by the pupil into its actual diameter.
[0005] The key problem with existing technology lies in its sensitivity to distance and angle. The scaling factor fails: the scaling factor during calibration depends on a fixed camera-eye distance (e.g., 30cm). If the distance or angle changes slightly during actual measurement (e.g., ±5cm or tilt), it will cause perspective distortion and changes in magnification: when the camera is tilted, the circular outline of the pupil becomes an ellipse in the image, increasing the diameter measurement deviation; increasing the distance will decrease the pupil's proportion in the image, and vice versa, requiring recalibration of the scaling factor.
[0006] Existing solutions using fixed supports require the subject to keep their head still, but this makes it difficult to completely eliminate minute movements. For example, the pupil meter disclosed in CN110123345A requires maintaining a strictly fixed distance. Dynamic calibration involves some systems using additional sensors (such as TOF ranging) to correct the scale in real time, but this increases hardware complexity. Multi-view compensation schemes use multiple cameras to reduce angular influence, but they are costly and have complex algorithms. For example, US2018 / 0153255 uses multi-camera calibration, which has a complex structure.
[0007] Fixed-stent pupil measurement solutions face significant challenges in various application scenarios. For example, rapid measurement is required in clinical settings (such as stroke assessment), but patient head movements are difficult to control. In wearable devices, head-mounted devices (such as VR glasses) experience distance fluctuations due to loose fit.
[0008] A Purchin spot is a light spot formed by the reflection of an optical fiber into different parts of the eyeball after it is incident on the pupil. For example, a bright spot can be formed on the outer surface of the cornea. This spot does not change with the movement of the eyeball, and its position and characteristics are repeatable. It can serve as a stable reference in various eye detection and analysis methods and has been applied in fields such as eye tracking and iris recognition.
[0009] Therefore, those skilled in the art are dedicated to developing a pupil diameter measurement method and device based on real-time calibration using Purchin spot images, in order to reduce the impact of distance and angle changes on the measurement results and improve the robustness of pupil measurement. Summary of the Invention
[0010] This application provides a method and apparatus for measuring pupil diameter based on real-time calibration. It utilizes point light sources with a fixed spacing L to form a reflective Purkinje spot on the cornea, and captures the image of this spot with a pixel spacing P using a camera. ref Real-time calculation of calibration coefficient K = L × β / P ref ; Measure the pupil pixel value P in the same image pupi1 Combining this with K, we obtain the actual pupil diameter D = K × P. pupil The technique of dynamically calibrating parameters has solved the technical problem of reducing the impact of distance and angle changes on the measurement results in pupil diameter measurement.
[0011] The specific technical solution of this application is described below.
[0012] In a first aspect, this application provides a method for measuring pupil diameter based on real-time calibration, the steps of which include:
[0013] (1) Two point light sources with a fixed distance of L are fixedly installed around the camera lens, and the light emitted by the point light sources is irradiated onto the corneal surface of the subject's eye to form a reflected light spot.
[0014] (2) Capture an image containing the eyes, pupils, and two corneal reflective spots using a camera;
[0015] (3) Measure the pixel distance P between two corneal reflective spot images in the image. ref ;
[0016] (4) Based on the known fixed spacing L and the measured pixel distance P ref Combined with the pre-calibrated correction coefficient β, the calibration coefficient K under the current measurement state is calculated in real time, where K=L×β / P ref The unit is mm / pixel; the correction coefficient β is determined through experimental calibration and is used to compensate for errors introduced by corneal curvature and optical system distortion;
[0017] (5) Measure the pixel value P corresponding to the pupil diameter in the same image. pupil ;
[0018] (6) Calculate the actual pupil diameter D using the calibration coefficient K, where D = K × P pupil .
[0019] Furthermore, a simulated pupil with a precise pupil diameter D0 is used, the surface of which has a transparent film to reflect and form a Purkinjet spot; an image I' of the simulated pupil is captured by a camera, and the pixel diameter D' of the simulated pupil and the pixel distance P of the spot image point are measured. ref The correction coefficient β is calculated based on D0 = β × D'.
[0020] Furthermore, the point light source is an infrared LED, whose wavelength matches the photosensitive band of the camera.
[0021] Furthermore, the real-time calculation of the calibration coefficient K and the pupil diameter measurement are performed in the same frame image.
[0022] Furthermore, the calibration coefficient K is used to reflect in real time the actual physical distance represented by one pixel in the image at the current camera position.
[0023] Furthermore, the pixel distance P between the Pulcyn spot image points ref and pupil pixel diameter P pupilThe results are calculated based on the center of the corneal reflective spot and the pupil boundary, which are located using an edge detection algorithm.
[0024] Furthermore, the spacing L of the point light source is 5-20mm.
[0025] Furthermore, the installation angle of the point light source is within the range of 50°-80° with the optical axis of the imaging system, and its relative position to the camera lens is rigidly fixed.
[0026] Through the above steps, the imaging ratio can be calibrated in real time and dynamically each time the pupil is measured, ensuring that the measurement results are not affected by slight changes in the relative position between the camera and the eye.
[0027] Secondly, this application provides a pupil diameter measurement device based on real-time calibration, implementing any of the pupil diameter measurement methods based on real-time calibration implemented in the first aspect, comprising: a camera module for capturing eye images; two point light sources with a fixed spacing L, symmetrically mounted around the camera lens, for generating corneal reflective Purkinjet spots; and an image processing module for detecting the reflected spots and the pupil edge, and calculating the pixel distance P between the reflected spots. ref and pupil pixel diameter P pupil ; Calibration calculation module, used to calculate P ref The calibration coefficient K is calculated in real time using L and the pre-stored correction coefficient β; the pupil diameter output module is used to output the actual pupil diameter D.
[0028] Furthermore, the spacing L of the point light sources is 5-20mm.
[0029] Furthermore, the angle between the point light source and the optical axis of the imaging system is in the range of 50°-80°, and its relative position to the camera lens is rigidly fixed.
[0030] Furthermore, the image processing module uses an edge detection algorithm to locate the center of the corneal reflective purchin spot and the pupil boundary.
[0031] Furthermore, the device also includes a display unit for displaying the calibration coefficient K and the pupil diameter measurement results in real time.
[0032] Furthermore, the point light source can be fixed in an array or embedded, or the infrared LED light source can be aligned with the camera's optical path using a beam splitter to achieve coaxial illumination.
[0033] The innovation of this invention lies in the fact that although changes in camera position cause variations in the calibration coefficient K, this coefficient, along with the ratio of the pupil diameter measurement to its pixel value, essentially follows the same physical laws. Therefore, by using K, which is calculated in real-time from a known fixed spacing and its imaging pixel values, the actual physical diameter corresponding to the pupil pixel value in the same image can be accurately and in real-time calibrated.
[0034] The core difference of this invention is the introduction of a reference light source with a known fixed spacing and its corneal reflection Pulcyn spot imaging, utilizing the image spacing P of the reference light source. ref Given a known physical distance L, the precise calibration coefficient K for the current camera position is calculated in real time within the same image at each measurement instant. This coefficient accurately reflects the impact of the current camera position on the imaging ratio and is applied to the measurement calculation of the pupil diameter in the same frame, fundamentally eliminating the measurement error of the pupil diameter caused by minute changes in the relative distance and angle between the camera and the eye.
[0035] The pupil diameter measurement method and device based on real-time calibration provided by this invention have the following significant technical effects:
[0036] 1) Significantly improve measurement accuracy: By dynamically and in real time marking the ratio between pixels and physical size during each measurement, the system error introduced by the slight changes in the relative distance and angle between the camera and the human eye is effectively eliminated, greatly improving the accuracy of pupil diameter measurement.
[0037] 2) Enhanced measurement reliability: Measurement results no longer depend on whether the operator can accurately maintain a fixed distance and angle, reducing the difficulty of operation and improving the consistency and reliability of different operators and multiple measurement results.
[0038] 3) Achieve dynamic adaptation: Even if the camera position is slightly disturbed during the measurement process (such as natural shaking of the handheld device), the system can compensate in real time to maintain measurement accuracy.
[0039] 4) Simple structure and easy to implement: It can be achieved by adding a fixed-interval point light source (such as infrared LED) to the existing pupil measuring instrument. The modification cost is low and it is easy to integrate into existing equipment or apply to the development of new equipment. Attached Figure Description
[0040] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.
[0041] Figure 1 The diagram shows the structure of the pupil diameter measurement method and device based on real-time calibration provided in Embodiments 1 and 2 of this application, illustrating the relative positions of the camera, point light source, and the eye being measured, as well as the relationship between pixels and physical parameters.
[0042] Figure 2 The experimental data curves for real-time calibration of K values at multiple distances between the camera and the eye are provided for embodiments 1 and 2 of this application.
[0043] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation
[0044] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.
[0045] The technical solution of this application and how it solves the above-mentioned technical problems will be described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will be described below with reference to the accompanying drawings.
[0046] Example 1
[0047] To clearly understand the technical solution of Embodiment 1 of this application, the solutions of the prior art will first be described in detail. Prior art typically relies on a one-time initial calibration or assumes that the relative position of the camera and the eye remains constant during measurement. When the actual position changes slightly (which is unavoidable during manual operation or operation by different measurers), the original pixel-physical size ratio becomes invalid, leading to measurement errors. Prior art lacks an online compensation mechanism for such dynamic position changes.
[0048] A Purchin spot is a light spot formed by the reflection of an optical fiber into different parts of the eyeball after it is incident on the pupil. For example, a bright spot can be formed on the outer surface of the cornea. This spot does not change with the movement of the eyeball, and its position and characteristics are repeatable. It can serve as a stable reference in various eye detection and analysis methods and has been applied in fields such as eye tracking and iris recognition.
[0049] Therefore, this invention application considers developing a pupil diameter measurement method and device based on real-time calibration using Purkinje spot images, in order to reduce the impact of distance and angle changes on the measurement results and improve the robustness of pupil measurement.
[0050] The core difference in Embodiment 1 of this invention is the introduction of a reference light source with a known fixed spacing and its corneal reflection imaging, utilizing the image spacing P of the reference light source. refGiven its known physical distance L, the precise calibration coefficient K for the current camera position is calculated in real time within the same image at each measurement instant. In such cases... Figure 2 In the experiment shown, the K-value was calibrated in real time at multiple distances between the camera and the eye. The distance between the camera and the eye was changed by 5mm each time, for a total of 7 positions. Here, m represents the ratio of the simulated human eye size to pixels, and n represents the ratio of the light spot spacing to pixels. It can be observed that m and n are completely correlated as the distance changes. Therefore, the coefficient K after real-time calibration changes by only 2% at different positions, effectively suppressing measurement errors caused by distance variations. Thus, this coefficient K can accurately reflect the influence of the current camera position on the image ratio in real time. Applying it to the measurement and calculation of pupil diameter in the same frame image can fundamentally eliminate the measurement error of pupil diameter caused by minute changes in the relative distance and angle between the camera and the eye.
[0051] In such Figure 1 Given the relative positions and pixel and physical parameter relationships of the camera, point light source, and the eye being measured, this embodiment 1 implements a pupil diameter measurement method based on real-time calibration. The steps include: 1) Introducing a reference light source: Two point light sources with a known fixed distance L are fixedly installed around the camera lens, and the light emitted by these two light sources is irradiated onto the eye.
[0052] 2) Utilizing corneal reflection: Light emitted from a light source is reflected on the surface of the cornea of the eye. These reflected light spots are also captured by the same camera and form two light spot images on the image.
[0053] 3) Measure the reference spacing pixel value: In the image captured by the camera, measure the pixel distance P between the two corneal reflective spot image points. ref .
[0054] 4) Calculate the real-time calibration coefficient: Since the actual physical distance L between the two point light sources is fixed, while their pixel distance P in the image is different... ref It changes with the distance and angle between the camera and the eye, so a calibration coefficient (K) can be calculated in real time:
[0055] K = βL / P ref
[0056] The unit of this coefficient K is mm / pixel. It reflects in real time the actual physical distance represented by one pixel in the image at the current camera position. β represents the correction coefficient.
[0057] 5) Pupil Measurement and Real-time Calibration: In the same image, measure the pixel value P corresponding to the pupil diameter. pupil .
[0058] 6) Calculate the actual pupil diameter: Using the calibration coefficient K obtained from real-time calculation, convert the pixel size of the pupil into the actual pupil diameter D.
[0059] D = P pupil ×K;
[0060] 7) The correction factor β is calibrated using a simulated pupil image. This image has a precise pupil diameter D0 and a transparent film on its surface for reflection to form a Purkinje spot. The camera simultaneously captures the simulated pupil and the Purkinje spot. The simulated pupil diameter D' is calculated according to the above process, and the correction factor is calculated according to D0=β×D'.
[0061] In Example 1, the pixel distance P between the Pulcyn spot image points ref It is calculated based on the edge detection algorithm to locate the center of the corneal reflective spot and the pupil boundary.
[0062] In Example 1, the spacing between the point light sources is 5mm, and the angle between the point light source installation angle and the optical axis of the imaging system is 50°.
[0063] In an improved embodiment of Example 1, the spacing between the point light sources is 20 mm, and the angle between the installation angle of the point light sources and the optical axis of the imaging system is 80°.
[0064] In another improved embodiment of Example 1, the spacing L of the point light sources is 12mm, and the angle between the installation angle of the point light sources and the optical axis of the imaging system is 60°.
[0065] Through the above steps, Embodiment 1 and its improved embodiments achieve real-time and dynamic calibration of the imaging ratio during each measurement, ensuring that the measurement results are not affected by minor changes in the relative position between the camera and the eye.
[0066] Example 2
[0067] In such Figure 1 Based on the method of Embodiment 1, and considering the relative positions and pixel and physical parameter relationships of the camera, point light source, and the eye being measured, Embodiment 2 implements a pupil diameter measurement device based on real-time calibration. The device includes: a camera module for capturing eye images; two point light sources with a fixed spacing L, symmetrically mounted around the camera lens to generate corneal reflective spots; and an image processing module for detecting the reflective spots and the pupil edge, and calculating the pixel distance P between the reflective spots. ref and pupil pixel diameter P pupil ; Calibration calculation module, used to calculate P ref The calibration coefficient K is calculated in real time with L; the pupil diameter output module is used to output the actual pupil diameter D.
[0068] In Example 2, the spacing L of the point light sources is 5mm, and their relative positions with the camera lens are rigidly fixed.
[0069] In Example 2, the angle between the point light source installation angle and the optical axis of the imaging system is 50°, and the angle between the point light source installation angle and the optical axis of the imaging system is 60°.
[0070] In Example 2, the image processing module uses an edge detection algorithm to locate the center of the corneal reflective spot and the pupil boundary.
[0071] In an improved embodiment of Example 2, the spacing L of the point light sources is 20mm, and the angle between the installation angle of the point light sources and the optical axis of the imaging system is 80°.
[0072] In another preferred embodiment of Example 2, the spacing L of the point light sources is 10 mm, and the angle between the installation angle of the point light sources and the optical axis of the imaging system is 65°.
[0073] In an improved embodiment of Example 2, the device further includes a display unit for displaying the calibration coefficient K and the pupil diameter measurement results in real time.
[0074] In an improved embodiment of Example 2, the point light source is fixed in an array.
[0075] In another preferred embodiment of Example 2, the point light source is embedded and fixed.
[0076] In another preferred embodiment of Example 2, the point light source uses a beam splitter to overlap the infrared LED light source with the camera's optical path to achieve coaxial illumination.
[0077] Through the above implementation methods, Example 2 and its various improved implementation methods realize real-time and dynamic calibration of the imaging ratio during each measurement, ensuring that the measurement results are not affected by slight changes in the relative position between the camera and the eye.
[0078] Through Examples 1 and 2, it can be seen that the innovation of this invention is that although changes in camera position cause changes in the calibration coefficient K, the ratio of this coefficient to the pupil diameter measurement and its pixel value essentially follows the same physical law, such as... Figure 2 As shown. Therefore, by using the known fixed spacing and the K calculated in real time from its imaging pixel values, the actual physical diameter corresponding to the pupil pixel value in the same image can be accurately and in real time determined.
[0079] The embodiments 1 and 2 and their improved embodiments provided by the present invention have the following significant technical effects:
[0080] 1) Significantly improve measurement accuracy: By dynamically and in real time marking the ratio between pixels and physical size during each measurement, the system error introduced by the slight changes in the relative distance and angle between the camera and the human eye is effectively eliminated, greatly improving the accuracy of pupil diameter measurement.
[0081] 2) Enhanced measurement reliability: Measurement results no longer depend on whether the operator can accurately maintain a fixed distance and angle, reducing the difficulty of operation and improving the consistency and reliability of different operators and multiple measurement results.
[0082] 3) Achieve dynamic adaptation: Even if the camera position is slightly disturbed during the measurement process (such as natural shaking of the handheld device), the system can compensate in real time to maintain measurement accuracy.
[0083] 4) Simple structure and easy to implement: It can be achieved by adding a fixed-interval point light source (such as infrared LED) to the existing pupil measuring instrument. The modification cost is low and it is easy to integrate into existing equipment or apply to the development of new equipment.
[0084] In the above embodiments, the descriptions of each embodiment have their own emphasis. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments. The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.
[0085] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this application are indicated by the following claims.
[0086] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.
Claims
1. A method for measuring pupil diameter based on real-time calibration, characterized in that, Includes the following steps: Two point light sources with a fixed distance L are rigidly fixed around the camera lens. The light emitted by the point light sources is irradiated onto the corneal surface of the subject's eye and forms a Purchin spot. The camera captures an image I containing the eye, pupil, and two corneal reflective Pulchin spots. The pixel distance P between two corneal reflective Pulcyn spot image points is measured in the image. ref ; Based on the known fixed spacing L and the measured pixel distance P ref Combined with the pre-calibrated correction coefficient β, the calibration coefficient K under the current measurement state is calculated in real time, where K = L × β / P ref The unit is mm / pixel; wherein, the correction coefficient β is determined by the following experimental calibration method: a simulated pupil with a precise pupil diameter D0 is used, the surface of which has a transparent film to reflect and form a Purkinje spot; The camera captures images of the simulated pupil, measures the pixel diameter D' of the simulated pupil and the pixel distance Pref' of the light spot image point, and calculates the result according to the formula β=(D0×Pref') / (L×D'), which is derived by combining D0=K×D′ and K=L×β / Pref′. This formula is used to compensate for errors introduced by corneal curvature and optical system distortion. The pixel value P corresponding to the pupil diameter is measured in image I. pupil ; The actual pupil diameter D is calculated using the calibration factor K, where D = K × P. pupil ; The point light source achieves coaxial illumination by aligning the infrared LED light source with the camera's optical path using a beam splitter.
2. The pupil diameter measurement method according to claim 1, characterized in that, The point light source is an infrared LED light, whose wavelength matches the photosensitive band of the camera.
3. The pupil diameter measurement method according to claim 1 or 2, characterized in that, The pixel distance P between the Pulcin spot image points ref and pupil pixel diameter P pupil The results are calculated based on the center of the corneal reflective spot and the pupil boundary, which are located using an edge detection algorithm.
4. A pupil diameter measuring device based on real-time calibration, implementing the measurement method as described in any one of claims 1-3, characterized in that, include: A camera module used to capture images of the eyes; Two point light sources with a fixed spacing of L are rigidly fixed and symmetrically installed around the camera lens to generate corneal reflective Purkinjet light spots. The point light sources achieve coaxial illumination by aligning the infrared LED light source with the camera optical path through a beam splitter. The image processing module is used to detect reflected light spots and pupil edges, and to calculate the pixel distance P between reflected light spots. ref and pupil pixel diameter P pupil ; The calibration calculation module is used to calculate P. ref The calibration coefficient K is calculated in real time using L and the correction coefficient β. The pupil diameter output module is used to output the actual pupil diameter D.
5. The pupil diameter measuring device according to claim 4, characterized in that, The spacing L of the point light sources is 5-20mm, and the installation angle is between 50° and 80° and the optical axis of the imaging system.
6. The pupil diameter measuring device according to claim 4, characterized in that, It also includes a display unit for real-time display of calibration coefficient K and pupil diameter measurement results.
7. The pupil diameter measuring device according to claim 4, characterized in that, The point light source is a fixed array.
8. The pupil diameter measuring device according to claim 4, characterized in that, The point light source is embedded and fixed.
Citation Information
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