Achromatic wave plate delay calculation method and system

Abstract

The present invention relates to the field of optical technology and discloses a method and system for calculating the delay of an achromatic wave plate to improve the real-time performance of the design and expand the universality of application scenarios. A The calculation method includes: obtaining the Jones matrix of the achromatic wave plate by multiplying the Jones matrices of each cascaded single wave plate; calculating the optical axis of the achromatic wave plate; after calculating the optical axis azimuth of the achromatic wave plate, multiplying the Jones matrix of the achromatic wave plate by the Jones vector of the linearly polarized light whose polarization direction is parallel to the optical axis of the achromatic wave plate to obtain the Jones vector of the transmitted light; dividing the Jones vector of the transmitted light by the Jones vector of the incident linearly polarized light parallel to the optical axis of the achromatic wave plate, the result obtained by calculation is the natural exponential function with the exponent of ; performing phase extraction on the calculated result, and then taking the absolute value, the result obtained is

Description

Technical Field

[0001] The present invention relates to the field of optical technology, and in particular to a method and system for calculating the delay of an achromatic wave plate. Background Art

[0002] Since the optical constants such as the refractive index of birefringent materials have a dispersion effect, traditional single-piece wave plates can only be used within a very small wavelength range. However, by combining multiple single-piece wave plates to form an achromatic wave plate, the achromatic function can be achieved within a wide wavelength range.

[0003] In the process of designing achromatic wave plates, it is necessary to calculate the delay of the achromatic wave plate and iterate multiple times to adjust the relevant parameters such as material, thickness, optical axis direction and angle. There are currently two commonly used methods for calculating the delay of achromatic wave plates. One method can only be used to calculate the cascaded symmetrical achromatic wave plates with an odd number of wave plates, and its universality is relatively poor. Although the other method can calculate the delay of achromatic wave plates with any number of wave plates, it uses the inverse tangent function in the final calculation of the delay, which limits the value range of the calculated delay. When designing an achromatic half-wave plate, the part of the calculated result exceeding 0.5λ will be folded downward with y=0.5λ as the symmetry axis, which is contrary to the actual situation. Therefore, the calculated result needs to be corrected again, which increases the amount of calculation and is more troublesome. Summary of the Invention

[0004] The present invention aims to disclose a method and system for calculating the delay of an achromatic wave plate, so as to improve the real-time performance of the design and expand the universality of application scenarios.

[0005] To achieve the above-mentioned purpose, the method for calculating the retardation of an achromatic wave plate disclosed in the present invention includes:

[0006] Step S1: multiply the Jones matrices of the cascaded wave plates to obtain the Jones matrix J of the achromatic wave plate. A (δ A ,θ A ); the calculation formula is:

[0007] J A (δ A ,θ A )=J n (δ n， θ n )J n-1 (δ n-1 ,θ n-1 )...J2(δ2, θ2)J1(δ1, θ1);

[0008] Among them, δ x The subscript x represents the delay of each wave plate, θ xIndicates the angle between the optical axis of each wave plate and the horizontal direction, except for δ A and θ A is unknown, while the retardation and optical axis azimuth of other wave plates are known; subscript A represents the entire achromatic wave plate, n is a positive integer greater than or equal to 2; x = 1, 2, ..., n, A;

[0009] The calculation formula for the optical axis azimuth of the achromatic wave plate is as follows:

[0010]

[0011] In the above formula, J A (1, 1) represents J A The element in the first row and first column of A (1, 2) represents J A The element in the first row and second column of ;

[0012] Step S2: Calculate the optical axis azimuth angle θ of the achromatic wave plate. A Finally, the Jones vector of the transmitted light is obtained by right-multiplying the Jones matrix of the achromatic wave plate by the Jones vector of the linearly polarized light whose polarization direction is parallel to the optical axis of the achromatic wave plate.

[0013] Step S3: Divide the Jones vector of the transmitted light by the Jones vector of the incident linearly polarized light parallel to the optical axis of the achromatic wave plate. The result is is the natural exponential function of the exponent;

[0014] Step S4: perform phase extraction on the result obtained in step S3 and then take the absolute value. The result is

[0015] Preferably, the method of the present invention further comprises:

[0016] Set the range and adjustment step of the known quantity parameters required in the above steps and the target delay of the achromatic wave plate, traverse various combinations of the known quantity parameters based on the adjustment step, calculate each combination one by one based on the above steps S1 to S5, and screen out various combinations whose calculation results are consistent with the target delay for display to the user.

[0017] To achieve the above objectives, the present invention also discloses a system for calculating the delay of an achromatic wave plate, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above method when executing the computer program.

[0018] The present invention has the following beneficial effects:

[0019] 1. Compared with the existing method for calculating the delay of achromatic wave plates, the method of the present invention has a wide range of applications and can be applied to achromatic wave plates with any number of cascaded wave plates, whether they have an odd or even number of plates.

[0020] 2. When calculating the retardation of achromatic wave plates, the Jones vector of linearly polarized light parallel to the optical axis of the achromatic wave plate is used for conversion, and the application of the inverse tangent function is avoided. The calculated results are accurate and require no further correction, which simplifies the calculation process and improves the timeliness of the calculation. In particular, during the solution optimization process, a single or multiple feasible solutions that meet the target retardation of the achromatic wave plate can be quickly selected based on iterative adjustment steps within the range of parameters such as thickness, optical axis direction, and angle.

[0021] The present invention will be described in further detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0023] Figure 1 This is a schematic structural diagram of an achromatic half-wave plate disclosed in an embodiment of the present invention.

[0024] Figure 2 yes Figure 1 The retardation curve of the achromatic half-wave plate shown in the figure is within the range of 300 to 1100 nm. DETAILED DESCRIPTION

[0025] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. However, the present invention can be implemented in many different ways as defined and covered by the claims.

[0026] Example 1

[0027] This embodiment discloses a method for calculating the retardation of an achromatic wave plate, comprising:

[0028] Step S1: multiply the Jones matrices of the cascaded wave plates to obtain the Jones matrix J of the achromatic wave plate. A (δ A ,θ A ); the calculation formula is:

[0029] J A (δ A ,θ A )=J n (δ n ,θ n )J n-1 (δ n-11 ,θn-1 )...J2(δ2, θ2)J1(δ1, θ1);

[0030] Among them, δ x The subscript x represents the delay of each wave plate, θ x Indicates the angle between the optical axis of each wave plate and the horizontal direction, except for δ A and θ A is unknown, while the retardation and optical axis azimuth of the other wave plates are known; the subscript A represents the entire achromatic wave plate, and n is a positive integer greater than or equal to 2; x = 1, 2, ... n ， A.

[0031] Furthermore, the calculation formula for the optical axis azimuth of the achromatic wave plate is as follows:

[0032]

[0033] In the above formula, J A (1, 1) represents J A The element in the first row and first column of A (1, 2) represents J A The elements in the first row and second column of are used to calculate the Jones matrix of the achromatic wave plate.

[0034] Step S2: Calculate the optical axis azimuth angle θ of the achromatic wave plate. A Finally, the Jones vector of the transmitted light is obtained by right-multiplying the Jones matrix of the achromatic wave plate with the Jones vector of the incident linearly polarized light whose polarization direction is parallel to the optical axis of the achromatic wave plate.

[0035] Step S3: Divide the Jones vector of the transmitted light by the Jones vector of the incident linearly polarized light parallel to the optical axis of the achromatic wave plate. The result is is the natural exponential function of the exponent.

[0036] Step S4: perform phase extraction on the result obtained in step S3 and then take the absolute value. The result is

[0037] Optionally, in this step, phase extraction can be performed based on MATLAB's own function angle.

[0038] Furthermore, the principle of the above calculation process is detailed as follows:

[0039] It is known that the Jones matrix of any wave plate can be expressed as:

[0040]

[0041] In the above formula, δ represents the retardation of the wave plate, and θ represents the azimuth of the wave plate optical axis, that is, the angle between the optical axis and the horizontal direction. For linearly polarized light with polarization along the θ direction, the Jones vector is:

[0042]

[0043] In the above formula, cosθ represents the horizontal component of linear polarized light, and sinθ represents the vertical component of linear polarized light. After the linear polarized light passes through the achromatic wave plate, the Jones vector expression of the transmitted light is J T Can be by J.J I Calculation, that is:

[0044]

[0045] The result of multiplying the above formula is still a determinant with two rows and one column, that is, The expression of S is:

[0046]

[0047] Using the sum-difference-product formula to simplify the expression in the brackets above, we can get:

[0048]

[0049] Then use Euler's formula to simplify again to get:

[0050]

[0051] Similarly, we can get:

[0052]

[0053] Thus, when the polarization direction of the incident linear polarized light is parallel to the optical axis of the achromatic wave plate, the Jones vector of the transmitted light is the Jones vector of the incident light multiplied by a factor of is the natural exponential function of the exponent.

[0054] In other words, this embodiment can also be regarded as selecting linearly polarized light whose polarization direction is parallel to the optical axis of the achromatic wave plate from among many incident relationships, and performing corresponding data conversion processing to simplify the calculation process of the delay amount of the achromatic wave plate, so that this selection achieves unexpected technical effects.

[0055] Furthermore, in this embodiment, based on the above-mentioned calculation process, the range of the known quantity parameters required in the above-mentioned steps and the adjustment step size and the target delay amount of the achromatic wave plate can be set, and various combinations of the known quantity parameters based on the adjustment step size are traversed. For each combination, calculations are performed one by one based on the above-mentioned steps S1 to S4, and various combinations whose calculation results are consistent with the target delay amount are screened out for display to the user.

[0056] Based on the above principles and processing steps, such as Figure 1 The example achromatic wave plate retardation calculation shown includes:

[0057] exist Figure 1 In the figure, there are two types of wave plates between the incident surface 1 and the exit surface 8; among them, the ones marked 1, 3, and 6 are quartz wave plates, and the ones marked 2, 4, and 5 are magnesium fluoride wave plates. The delay of each quartz wave plate is 10.9*λ@475nm, and the delay of each magnesium fluoride wave plate is 11.4*λ@475nm. The optical axes of quartz wave plate 1 and magnesium fluoride wave plate 2 are perpendicular to each other, the optical axes of quartz wave plate 3 and magnesium fluoride wave plate 4 are perpendicular to each other, and the optical axes of quartz wave plate 6 and magnesium fluoride wave plate 5 are perpendicular to each other. As long as it is confirmed The directions of the optical axes of quartz wave plates 1, quartz wave plates 3, and quartz wave plates 6 are determined, and the directions of the optical axes of the magnesium fluoride wave plates are also determined accordingly. The optical axis of quartz wave plate 1 is parallel to the optical axis of quartz wave plate 6. There is an angle between the optical axis of quartz wave plate 1 and the optical axis of quartz wave plate 3, which is 45 to 60 degrees. Transmissive films (@300 to 1100 nm) are coated on the incident and exit surfaces to improve the transmittance. The above steps can be used to calculate the retardation of the achromatic wave plate corresponding to this design in the range of 300 to 1100 nm as follows: Figure 2 As shown, the calculated delay error of the achromatic half-wave plate is less than ±X / 100.

[0058] Example 2

[0059] Corresponding to the above embodiment, this embodiment discloses a system for calculating the delay of an achromatic wave plate, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above method when executing the computer program.

[0060] In summary, the method and system disclosed in the above embodiments of the present invention have at least the following beneficial effects:

[0061] 1. Compared with the existing method for calculating the delay of achromatic wave plates, the method of the present invention has a wide range of applications and can be applied to achromatic wave plates with any number of cascaded wave plates, whether they have an odd or even number of plates.

[0062] 2. When calculating the retardation of achromatic wave plates, the Jones vector of linearly polarized light parallel to the optical axis of the achromatic wave plate is used for conversion, and the application of the inverse tangent function is avoided. The calculated results are accurate and require no further correction, which simplifies the calculation process and improves the timeliness of the calculation. In particular, during the solution optimization process, a single or multiple feasible solutions that meet the target retardation of the achromatic wave plate can be quickly selected based on iterative adjustment steps within the range of parameters such as thickness, optical axis direction, and angle.

[0063] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for calculating the delay of an achromatic wave plate, characterized in that: include: Step S1: multiply the Jones matrices of the cascaded wave plates to obtain the Jones matrix J of the achromatic wave plate. A (δ A ,θ A ); the calculation formula is: J A (d A ,i A )=J n (d n ,i n )J n-1 (d n-1 ,i n-1 )…J2(δ2,θ2)J1(δ1,θ1); Among them, δ x The subscript x represents the delay of each wave plate, θ x Indicates the angle between the optical axis of each wave plate and the horizontal direction, except for δ A and θ A is unknown, while the retardation and optical axis azimuth of other wave plates are known; subscript A represents the entire achromatic wave plate, n is a positive integer greater than or equal to 2; x = 1, 2, ..., n, A; The calculation formula for the optical axis azimuth of the achromatic wave plate is as follows: In the above formula, J A (1,1) represents J A The element in the first row and first column of A (1,2) represents J A The element in the first row and second column of ; Step S2: Calculate the optical axis azimuth angle θ of the achromatic wave plate. A Finally, the Jones vector of the transmitted light is obtained by right-multiplying the Jones matrix of the achromatic wave plate by the Jones vector of the linearly polarized light whose polarization direction is parallel to the optical axis of the achromatic wave plate. Step S3: Divide the Jones vector of the transmitted light by the Jones vector of the incident linearly polarized light parallel to the optical axis of the achromatic wave plate. The result is is the natural exponential function of the exponent; Step S4: perform phase extraction on the result obtained in step S3 and then take the absolute value. The result is 2. The method according to claim 1, characterized in that Also includes: Set the range and adjustment step of the known quantity parameters required in the above steps and the target delay of the achromatic wave plate, traverse various combinations of the known quantity parameters based on the adjustment step, calculate each combination one by one based on the above steps S1 to S5, and screen out various combinations whose calculation results are consistent with the target delay for display to the user.

3. A system for calculating the delay of an achromatic wave plate, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the method according to claim 1 or 2 is implemented.

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