CN110927965B - Design method of compensation lens for compensating error caused by light deflection - Google Patents
Design method of compensation lens for compensating error caused by light deflection Download PDFInfo
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- 239000000463 material Substances 0.000 claims description 7
- 238000005259 measurement Methods 0.000 claims description 5
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Abstract
The invention discloses a method for compensating errors caused by light deflectionThe design method of the compensation lens comprises the following steps: in y'ij‑yiThe incident angle theta is preset under the condition that | is less than delta yjModifying a related parameter iterative computation optimization function M, and taking a minimum value; the relevant parameters are: distance d from reference surface to surface of compensation lens far from flat glass side0Thickness d of the compensation lens1Distance d between the compensation lens and the flat glass2Refractive index of compensation lens, and radius of curvature r of both surfaces of compensation lens1、r2(ii) a Y 'when M is minimum'ijThe corresponding related parameters are compensation lens parameters;
wherein, assuming that the optical path does not include the compensation lens and the flat glass, the incident light is on the photosensitive surfaceiIs imaged, when the coordinate of the incident light on the reference surface is yij；y′ijTo pass through the position yijUnder the action of the compensating lens and the flat glass, the incident light is projected to a point on the photosensitive surface; q. q.siIs a weight; Δ y is a preset deviation threshold. The compensating lens designed by the method can reduce the offset of the light reaching the photosensitive surface by at least 60%.
Description
Technical Field
The invention relates to the field of optical element design, in particular to a design method of a compensation lens for compensating errors caused by light deflection.
Background
The photoelectric detector can convert optical signals into electric signals when working, and has wide application in various fields of military and national economy, for example, in a measuring system utilizing structured light, a laser device realizes scanning of signal light by rotating or repeatedly moving up, down, left and right, and the accurate position of a measured object is judged by the time of scanning light reaching a photosensitive surface. The outer surface of the existing photoelectric detector is provided with plate glass for protecting an internal photosensitive surface, light rays can be deflected after passing through the plate glass, the offset of the light rays is related to the thickness and the incident angle of the plate glass, and the offset can seriously affect the precision of a measuring result for a precision measuring system; therefore, the offset needs to be reduced by adopting a technical means, and a common method is to select a photoelectric detector with small protective glass thickness, but the method cannot meet a system with special requirements and does not have universality.
Disclosure of Invention
In order to solve the above-mentioned problems, the present invention provides a method for designing a compensation lens for compensating an error caused by light deflection, which compensates the error caused by light deflection by adding a lens or replacing a flat glass with a globe. The specific technical scheme is as follows:
a design method of compensating lens for compensating error caused by light deflection is disclosed, the compensating lens is used for compensating error caused by light deflection generated on the photosensitive surface by plate glass; the method is characterized by comprising the following steps:
in y'ij-yiF incident angles theta are preset under the condition that | < delta yjModifying related parameters to iteratively calculate an optimization function M, and taking the minimum value; y 'when M is minimum'ijThe corresponding related parameters are compensation lens parameters;
wherein, yiRepresenting different positions on the photosensitive surface, i is 1,2 … … m; assuming that the light path does not include a compensation lens and a plate glass, m light rays are incident no matter what the incident angle is, and the m positions y correspond to the photosensitive surfaceiIs imaged, when the coordinate of the incident light on the reference surface is yij；
y′ijTo pass through the position yijUnder the action of the compensating lens and the flat glass, the incident light is projected to a point on the photosensitive surface; q. q.siFor different positions y on the photosensitive surfaceiThe corresponding weight;
Δ y is a preset deviation threshold;
when the optimization function M is calculated in an iterative manner, the modified relevant parameters are as follows: distance d from reference surface to surface of compensation lens far from flat glass side0Thickness d of the compensation lens1The distance d between the compensation lens close to the flat glass and the flat glass2Refractive index of compensation lens, and radius of curvature r of both surfaces of compensation lens1、r2。
Further: y'ij＝L5ijtanU5ij
Wherein, U5ijFor the ith strip at an incident angle thetajIncident light reaches the light sensorThe angle between the rear surface (the 5 th surface) and the optical axis; l is5ijFor the ith strip at an incident angle thetajThe distance between the intersection point of the incident light and the optical axis and the photosensitive surface;
L5ij、U5ijobtaining the following components by formulas (I) - (C):
formula (I)
Formula 2
Formula ③ U'kij＝Ukij+αkij-α′kij(ii) a Formula iv
Formula (v) L(k+1)ij＝L'kij-dk(ii) a Formula (U)(k+1)ij＝U′kij；
Formula (c)
k is selected from 1,2,3 and 4; two surfaces of the compensation lens and two surfaces of the flat glass are represented in sequence along the direction of incident light;
Lkijis the intersection point of the kth plane and the optical axis and the ith strip at an incident angle thetajThe distance between the intersection point of the extension line of the incident light ray incident on the kth surface and the optical axis;
Lkij' is the intersection point of the kth plane and the optical axis and the ith strip at an incident angle thetajThe distance between the intersection point of the extension line of the incident light ray after being emitted from the kth surface and the optical axis;
αkijfor the ith strip at an incident angle thetajThe incident light is transmitted to the angle between the kth surface and the normal of the kth surface;
α′kijfor the ith strip at an incident angle thetajThe included angle between the incident light and the normal of the kth surface when the incident light is emitted from the kth surface;
Ukijfor the ith strip at an incident angle thetajThe incident light transmits to the k-th surface and forms an included angle with the optical axis; by definition, U1ij＝θj；
U'kijFor the ith strip at an incident angle thetajThe included angle between the incident light and the optical axis when the incident light is emitted from the kth surface;
rkis the radius of curvature of the kth face;
nkis the object-side refractive index of the kth face; n isk' is the image-side refractive index of the kth face;
d3is the thickness of the sheet glass; d4The distance between the plate glass and the photosensitive surface; simultaneously: d0+d1+d2+d3+d4The value of (d) is a predetermined constant.
Further: obtaining L through formulas (I) - (III)5ij、U5ijThe method comprises the following steps:
first is d0、d1、d2、r1、r2Setting an initial value, n being set according to the lens materialk、nk'; then according to formula (c) to obtain L1ijCombining formulas from (I) to (IV) to obtain alpha1ij、α′1ij、U′1ij、L′1ijThen, according to the formula, # and # obtain L2ij、U2ij(ii) a Iterative calculation is carried out by adopting the same method to obtain L5ij、U5ij。
Further: when Zemax is used for calculation, the formula
Is replaced by
In the formula: vf×(j-1)+i＝y′ij、Tm×(j-1)+i＝yi、Qm×(j-1)+i＝qi；
x represents a certain point, Q is a weight, V is an actual measurement value, and T is a target value.
Further: when d is3When equal to 0, r1-r2Is constant.
Further: m is 3, y1、y2、y3Respectively located at the upper, middle and lower positions of the photosensitive surface.
The invention provides a design method of a compensation lens for compensating errors caused by light deflection, which can compensate the precision of projecting incident light at multiple angles and random angles to a photosensitive surface of a detector, taking light with the thickness of 1mm and the incident angle of 60 degrees as an example, the offset of the light on the photosensitive surface is about 1mm, which can cause the displacement error of a measured object to be 1mm, and is a considerable measurement error for a system with the measurement precision of a silk-meter level; after the compensating lens designed according to the method provided by the invention is added, the light ray offset of each incident angle is reduced by at least 60%.
Drawings
FIG. 1 is a schematic view of the design concept of example 1;
FIG. 2 is a schematic view showing light transmission from a single surface in example 1;
FIG. 3 is a schematic view of the design concept of example 2.
Detailed Description
The technical solution of the present invention is described in detail below with reference to the accompanying drawings and examples.
Example 1
A design method of compensating lens for compensating error caused by light deflection is disclosed, the compensating lens is used for compensating error caused by light deflection generated on the photosensitive surface by plate glass; the method comprises the following steps:
in y'ij-yiF incident angles theta are preset under the condition that | < delta yjModifying related parameters to iteratively calculate an optimization function M, and taking the minimum value; y 'when M is minimum'ijThe corresponding related parameters are compensation lens parameters;
wherein, yiRepresenting different positions on the photosensitive surface, i is 1,2 … … m; assuming that the light path does not include a compensation lens and a plate glass, m light rays are incident no matter what the incident angle is, and the m positions y correspond to the photosensitive surfaceiIs imaged, when the coordinate of the incident light on the reference surface is yij(ii) a In this embodiment, m is 3, y1、y2、y3Are respectively positioned at the upper, middle and lower positions of the photosensitive surface, and the coordinate on the reference surface corresponding to the light ray is y1j、y2j、y3jAs shown in fig. 1;
y′ijto pass through the position yijUnder the action of the compensating lens and the flat glass, the incident light is projected to a point on the photosensitive surface; q. q.siFor different positions y on the photosensitive surfaceiThe corresponding weight;
Δ y is a preset deviation threshold;
when the optimization function M is calculated in an iterative manner, the modified relevant parameters are as follows: distance d from reference surface to surface of compensation lens far from flat glass side0Thickness d of the compensation lens1The distance d between the compensation lens close to the flat glass and the flat glass2Refractive index of compensation lens, and radius of curvature r of both surfaces of compensation lens1、r2。
Specifically, y'ij＝L5ijtanU5ij
Wherein, U5ijFor the ith strip at an incident angle thetajThe incident light reaches the photosensitive surface and forms an included angle with the optical axis; l is5ijFor the ith strip at an incident angle thetajThe distance between the intersection point of the incident light and the optical axis and the photosensitive surface;
L5ij、U5ijobtaining the following components by formulas (I) - (C):
formula (I)
Formula 2
Formula ③ U'kij＝Ukij+αkij-α'kij(ii) a Formula iv
Formula (v) L(k+1)ij＝L'kij-dk(ii) a Formula (U)(k+1)ij＝U'kij；
Formula (c)
k is selected from 1,2,3 and 4; two surfaces of the compensation lens and two surfaces of the flat glass are represented in sequence along the direction of incident light;
Lkijis the intersection point of the kth plane and the optical axis and the ith strip at an incident angle thetajThe distance between the intersection point of the extension line of the incident light ray incident on the kth surface and the optical axis;
Lkij' is the intersection point of the kth plane and the optical axis and the ith strip at an incident angle thetajThe distance between the intersection point of the extension line of the incident light ray after being emitted from the kth surface and the optical axis;
αkijfor the ith strip at an incident angle thetajThe incident light is transmitted to the angle between the kth surface and the normal of the kth surface;
α′kijfor the ith strip at an incident angle thetajThe included angle between the incident light and the normal of the kth surface when the incident light is emitted from the kth surface;
Ukijfor the ith strip at an incident angle thetajThe incident light transmits to the k-th surface and forms an included angle with the optical axis;
U'kijfor the ith strip at an incident angle thetajThe included angle between the incident light and the optical axis when the incident light is emitted from the kth surface;
rkis the radius of curvature of the kth face;
nkis the object-side refractive index of the kth face; n isk' is the image-side refractive index of the kth face;
d3is the thickness of the sheet glass; d4The flat glass is spaced from the photosensitive surfaceThe distance between them; simultaneously: d0+d1+d2+d3+d4The value of (d) is a predetermined constant.
When calculating: first is d0、d1、d2、r1、r2Setting an initial value, n being set according to the lens materialk、nk'; then according to formula (c) to obtain L1ijCombining formulas from (I) to (IV) to obtain alpha1ij、α′1ij、U′1ij、L′1ijThen, according to the formula, # and # obtain L2ij、U2ij(ii) a Iterative calculation is carried out by adopting the same method to obtain L5ij、U5ij。
In the calculation process, the calculation can be performed through programming software such as Matlab and the like, and the optimization can also be performed through optical software such as Zemax, Code V and the like.
When Zemax is used for calculation, the formula
Is replaced by
In the formula: vf×(j-1)+i＝y′ij、Tm×(j-1)+i＝yi、Qm×(j-1)+i＝qi(ii) a x represents a certain point, Q is a weight, V is an actual measurement value, and T is a target value.
As shown in fig. 1, it is assumed that the diameter of the photosensitive surface is 1mm, the distance from the photosensitive surface to the plate glass is 1mm, and the thickness of the plate cover glass is 1 mm. A spherical lens is used to compensate the deflection of the plate. Table 1 shows the optical path parameters, and table 2 shows that the offset when no compensation lens is added is compared with the offset when no compensation lens is added, and the offset between the light beam reaching the surface of the photosensitive surface and the position where the light beam directly irradiates on the photosensitive surface is much lower than the data when no compensation lens is added.
Table 1: optical path parameters
| Flour mark | Radius of curvature | Thickness or spacing | Material | Remarks for |
| 1 | Infinity | 0.500 | |
|
| 2 | 13.222 | 1.500 | H-K9L | Spherical surface, r1, |
| 3 | 13.694 | 6.001 | Spherical surface, r2, |
|
| 4 | Infinity | 1.000 | H-K9L | Sheet cover glass, |
| 5 | Infinity | 1.000 | |
Note: the refractive index of material H-K9L was 1.5168.
Table 2: offset comparison with and without spherical compensating lens
Example 2
This example differs from example 1 in that: when d is3When equal to 0, r1-r2The constant (namely concentric circles) is to replace the flat glass by a spherical cover. Will d3＝0，r1-r2The equation (r) is combined with the constant (r) to (c) to calculate and solve, and tables 3 and 4 show an optimization result, where the distance from a certain point on the spherical surface to the photosensitive surface is defined as r2. Therefore, the ball cover designed by the method can greatly reduce the influence of light deflection on the detection result.
Table 3: parameters of the ball cover
| k | Radius of curvature | Thickness or spacing | Material | Remarks for |
|
| 1 | Infinity | 0.500 | |
||
| 2 | 9.525 | 1.500 | H- | Spherical surface | |
| 3 | 8.025 | 8.000 | |
||
| 4 | Infinity | 0.000 | Photosensitive surface |
Note: the refractive index of material H-K9L was 1.5168.
Table 4: offset after replacing plate glass with spherical cover
The foregoing descriptions of specific exemplary embodiments of the present invention have been presented for purposes of illustration and description. The foregoing description is not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The exemplary embodiments were chosen and described in order to explain certain principles of the invention and its practical application to enable others skilled in the art to make and use various exemplary embodiments of the invention and various alternatives and modifications thereof. It is intended that the scope of the invention be defined by the following claims and their equivalents.
Claims (4)
1. A design method of compensating lens for compensating error caused by light deflection is disclosed, the compensating lens is used for compensating error caused by light deflection generated on the photosensitive surface by plate glass; the method is characterized by comprising the following steps:
in y'ij-yiF incident angles theta are preset under the condition that | < delta yjModifying related parameters to iteratively calculate an optimization function M, and taking the minimum value; y 'when M is minimum'ijThe corresponding related parameters are compensation lens parameters;
wherein, yiRepresenting different positions on the photosensitive surface, i is 1,2 … … m; assuming that the light path does not include a compensation lens and a plate glass, m light rays are incident no matter what the incident angle is, and the m positions y correspond to the photosensitive surfaceiIs imaged, when the coordinate of the incident light on the reference surface is yij；
y′ijTo pass through the position yijUnder the action of the compensating lens and the flat glass, the incident light is projected to a point on the photosensitive surface; q. q.siFor different positions y on the photosensitive surfaceiThe corresponding weight;
Δ y is a preset deviation threshold;
when the optimization function M is calculated in an iterative manner, the modified relevant parameters are as follows: distance d from reference surface to surface of compensation lens far from flat glass side0Thickness d of the compensation lens1The distance d between the compensation lens close to the flat glass and the flat glass2Refractive index of compensation lens, and radius of curvature r of both surfaces of compensation lens1、r2；
y′ij＝L5ij tanU5ij
Wherein, U5ijFor the ith strip at an incident angle thetajThe incident light reaches the photosensitive surface and forms an included angle with the optical axis; l is5ijFor the ith strip at an incident angle thetajThe distance between the intersection point of the incident light and the optical axis and the photosensitive surface;
L5ij、U5ijobtaining the following components by formulas (I) - (C):
formula (I)
Formula 2
Formula ③ U'kij＝Ukij+αkij-α′kij(ii) a Formula iv
Formula (v) L(k+1)ij＝L′kij-dk(ii) a Formula (U)(k+1)ij＝U′kij；
Formula (c)
k is selected from 1,2,3 and 4; two surfaces of the compensation lens and two surfaces of the flat glass are represented in sequence along the direction of incident light;
Lkijis the intersection point of the kth plane and the optical axis and the ith strip at an incident angle thetajThe distance between the intersection point of the extension line of the incident light ray incident on the kth surface and the optical axis;
Lkij' is the intersection point of the kth plane and the optical axis and the ith strip at an incident angle thetajThe distance between the intersection point of the extension line of the incident light ray after being emitted from the kth surface and the optical axis;
αkijfor the ith strip at an incident angle thetajThe incident light is transmitted to the angle between the kth surface and the normal of the kth surface;
α′kijfor the ith strip at an incident angle thetajThe included angle between the incident light and the normal of the kth surface when the incident light is emitted from the kth surface;
Ukijfor the ith strip at an incident angle thetajThe incident light transmits to the k-th surface and forms an included angle with the optical axis;
U′kijfor the ith strip at an incident angle thetajThe included angle between the incident light and the optical axis when the incident light is emitted from the kth surface;
rkis the radius of curvature of the kth face;
nkis the object-side refractive index of the kth face; n isk' is the image-side refractive index of the kth face;
d3is the thickness of the sheet glass; d4The distance between the plate glass and the photosensitive surface; simultaneously: d0+d1+d2+d3+d4The value of (a) is a preset constant;
obtaining L through formulas (I) - (III)5ij、U5ijThe method comprises the following steps:
first is d0、d1、d2、r1、r2Setting an initial value, n being set according to the lens materialk、nk'; then according to formula (c) to obtain L1ijCombining formulas from (I) to (IV) to obtain alpha1ij、α′1ij、U′1ij、L′1ijThen, according to the formula, # and # obtain L2ij、U2ij(ii) a Iterative calculation is carried out by adopting the same method to obtain L5ij、U5ij。
2. A method as claimed in claim 1, wherein the method further comprises: when Zemax is used for calculation, the formula
Is replaced by
In the formula: vf×(j-1)+i＝y′ij、Tm×(j-1)+i＝yi、Qm×(j-1)+i＝qi；
x represents a certain point, Q is a weight, V is an actual measurement value, and T is a target value.
3. A method as claimed in claim 1, wherein the method further comprises: when d is3When equal to 0, r1-r2Is constant.
4. A method as claimed in claim 1, wherein the method further comprises: m is 3, y1、y2、y3Respectively located at the upper, middle and lower positions of the photosensitive surface.
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| CN106989749A (en) * | 2017-04-10 | 2017-07-28 | 中国船舶重工集团公司第七0七研究所 | A kind of method for eliminating paper chart glass refraction error |
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| CN102590988A (en) * | 2012-03-19 | 2012-07-18 | 苏州大学 | Compensator camera lens for aspheric surface detection |
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