JP5211656B2 - Toroidal surface evaluation method - Google Patents

Description

  The present invention relates to a toroidal surface evaluation method for evaluating the shape of a toroidal surface (also referred to as a toric surface) such as a toroidal mirror used in various optical devices and optical measuring devices.

  The concave toroidal mirror whose reflecting surface is aspherical has a feature that it can collect obliquely incident light from a point light source while suppressing astigmatism. Therefore, it is widely used in systems incorporating various optical measuring devices such as spectrophotometers and optical reading mechanisms.

  As shown in FIG. 1, the shape of the toroidal surface 2 that is generally the reflecting surface of the concave toroidal mirror 1 has two radii of curvature in the direction along the X axis and Y axis perpendicular to each other, that is, the curvature in the horizontal direction. It is expressed by parameters such as a radius Rh and a radius of curvature Rv in the vertical direction. In addition, the rotation of the shaft, more specifically, the rotation of the X axis and the Y axis around the Z axis orthogonal to the X axis and the Y axis (see FIG. 2A), the inclination of the axis (X axis) (Shift of perpendicularity between Y axis and Y axis) (see FIG. 2B) also affects the light condensing characteristics, and these can also be said to be parameters expressing the shape of the toroidal surface 2. In order for the concave toroidal mirror 1 to achieve a desired light collecting characteristic, it is necessary to manufacture the toroidal mirror 1 so that the parameters as described above fall within a predetermined tolerance range based on the specification value (design value). is there.

  Conventionally, as a method for evaluating the shape of the toroidal surface of the manufactured toroidal mirror, measurement using an optical interferometer and measurement using a contact type or non-contact type surface shape measuring instrument are generally used (for example, patents). Reference 1 and non-patent reference 1). However, with such a conventional method, it has been difficult to obtain the above parameters with sufficiently high accuracy.

Japanese Unexamined Patent Publication No. 6-13132 Shigeki Kato, “Aspherical Optical Element Toroidal Mirror”, Shimazu Review, Vol. 64, No. 1, Issue 2, September 28, 2007

  The present invention has been made to solve the above-described problems, and an object of the present invention is to provide an evaluation method capable of evaluating the shape of a toroidal surface such as a reflecting surface of a concave toroidal mirror with high accuracy. That is.

Toroidal surface evaluation method according to the present invention made to solve the above problems,
the measured obtaining a shape of the measured values of the toroidal surface and the shape measured by the three-dimensional measurement method of the contact or contactless a toroidal surface of a) evaluated,
Set the range of tolerance centered on the specifications of the parameters representing the shape of the toroidal surface of b) the evaluation as a change range of the provisional value of the parameter, while varying said tentative value within said alteration range, An optimization step of calculating a difference between the shape of the toroidal ideal surface calculated from the provisional value and the shape of the actual measurement value, and obtaining a provisional value that minimizes an evaluation value based on the difference;
c) an output step of outputting the temporary value finally obtained by the optimization step as a calculation result of the parameter;
It is characterized by including.

  Here, the parameters expressing the shape of the toroidal surface are the radius of curvature in the horizontal direction, the radius of curvature in the vertical direction, the rotation of the shaft, the inclination of the shaft, or the equivalent thereof, for example, the squareness of the shaft, etc. can do.

  As the three-dimensional measurement method, various conventionally known methods such as an interferometer and a non-contact (optical) three-dimensional measurement device can be used.

  The evaluation value based on the difference between the tentative value and the actual measurement value of the parameter may use the PV value (difference between the maximum point and the minimum point) as the simplest, but preferably the least square method It is good to use the average value by.

  According to the toroidal surface evaluation method according to the present invention, although not a direct measurement, the above-described parameters expressing the toroidal surface shape are within the tolerance range based on the specification value that is the ideal surface shape. The most probable value can be calculated. In particular, a concave toroidal mirror usually has different tolerances depending on the radius of curvature, but it is possible to calculate parameters with high accuracy in consideration of such tolerance differences. Thereby, for example, the surface shape of the manufactured concave toroidal mirror can be grasped with high accuracy, and can be widely used for development and management of manufacturing processes, evaluation and management of products, and the like.

Hereinafter, an embodiment of the toroidal surface evaluation method according to the present invention will be described with reference to the flowchart of FIG.
With respect to the toroidal surface to be evaluated, a specification value (design value) at the time of manufacturing the toroidal surface and a tolerance that defines the degree of deviation from the specification value are given as information in advance.

  First, for the toroidal surface to be evaluated, shape measurement is performed using, for example, a non-contact three-dimensional measuring instrument (step S1), and actual measurements such as horizontal curvature radius, vertical curvature radius, shaft rotation, and shaft inclination are performed. Value data is acquired (step S2). The shape measurement method is not particularly limited as long as necessary actual measurement data is obtained. Of course, the inclination of the shaft is the same as the perpendicularity of the shaft. In many cases, the actual values obtained in this way are not actually very accurate.

  Next, a calculation process using the measured value is executed. The subsequent calculation processing can be executed by, for example, operating a dedicated program on a general-purpose personal computer and giving the measured value, specification value, tolerance, etc. as input information.

  First, the two parameters of shaft rotation and inclination are fixed to the above-mentioned specification values, and the other two parameters, that is, the provisional values of the curvature radii Rh and Rv are set within a tolerance range around the respective specification values. The PV value of the difference between the temporary value and the actual measurement value is calculated for each change. Then, the PV values obtained sequentially are compared, and provisional values of the curvature radii Rh and Rv giving the minimum PV value are obtained (steps S3 and S4). The temporary values obtained at this time are Rhop and Rvop, respectively.

  Next, the values of the curvature radii Rh and Rv are fixed to the above Rhop and Rvop, and the provisional values of the remaining two parameters, that is, the rotation and inclination of the shaft, are determined within a tolerance range centered on the respective specification values. The PV value of the difference between the provisional value and the actual measurement value is calculated for each change. Then, the PV values obtained sequentially are compared, and provisional values of rotation and inclination of the shaft that give the minimum PV value are obtained (steps S5 and S6).

  Since the temporary values of the parameters finally obtained in steps S4 and S6 are considered to be values that most accurately represent the shape of the toroidal surface to be evaluated, these temporary values are used as the final calculation results. For example, it is displayed on a display screen of a personal computer (step S7). This completes the calculation process.

  In the above description, the PV value of the difference between the actually measured value and the provisional value is used as the evaluation value. However, it is more preferable to use an evaluation value that takes into account variations and noises such as an average value by the least square method. Good.

  In the above procedure, first, the temporary value of the curvature radius is changed after fixing the rotation and inclination of the shaft to the specification value, and then the temporary value of the rotation and inclination of the shaft is changed by fixing the curvature radius. However, this is because the calculation becomes complicated if all four provisional values are changed, and it is clear that the procedure is not limited to the above. For example, the radius of curvature is fixed to the specification value first, the provisional value for changing the provisional value of the rotation and inclination of the shaft to obtain the minimum PV value is obtained, and then the rotation and inclination of the shaft are fixed. The provisional value that gives the minimum PV value may be obtained by changing the provisional value of the two curvature radii. Alternatively, the provisional values of the four parameters may be sequentially changed one by one to obtain the provisional values that give the minimum PV values.

  In the above description, the toroidal surface is actually measured with a three-dimensional measuring instrument and then calculation processing is performed with a personal computer. However, these are systematized and automatically calculated using the results measured by the three-dimensional measuring means. It is also possible to construct an evaluation system that performs processing and outputs a calculation result. It is also possible to provide a program for executing the above-described calculation processing on a general-purpose personal computer.

A specific application example of the toroidal surface evaluation method of the above-described embodiment will be described.
The specifications of the toroidal surface to be evaluated are: horizontal curvature radius Rh: 282.8 (mm), vertical curvature radius Rv: 141.4 (mm), curvature radius tolerance: 2%, shaft perpendicularity: 90 °, shaft perpendicularity tolerance: ± 15 ', axis inclination: 0 °, axis inclination tolerance: ± 15'. That is, the parameters representing the shape of the ideal toroidal surface are as follows: horizontal curvature radius Rh: 282.8 (mm), vertical curvature radius Rv: 141.4 (mm), shaft rotation: 0 °, shaft perpendicularity: 90 °, It is.

  When the difference between the measured value obtained by measuring this toroidal surface with a three-dimensional measuring device (non-contact three-dimensional measuring device NH-3N manufactured by Mitaka Kogyo Co., Ltd.) and the above specification value is obtained, it is about 19.5λ. (Λ = 632.8 nm). FIG. 4A shows a three-dimensional display of the difference in shape at this time.

  The provisional value of the parameter was changed within the tolerance range from the specification value, and the provisional value that minimizes the PV value was obtained. As a result, horizontal curvature radius Rh: 285.48 (mm), vertical curvature radius Rv: 143.52 (mm), shaft rotation: -11 ', shaft squareness: 90 ° -9', PV value is the smallest Of 1.143λ. FIG. 4B shows the three-dimensional display of the difference in shape at this time.

  If FIG. 4B is compared with FIG. 4A, it can be understood that the difference is greatly reduced. This means that the provisional value giving the minimum PV value more accurately represents the actual toroidal surface parameter. The provisional values finally obtained in this way, that is, the radius of curvature Rh in the horizontal direction: 285.48 (mm), the radius of curvature in the vertical direction Rv: 143.52 (mm), the rotation of the shaft: −11 ′, and the perpendicularity of the shaft: 90 ° − 9 ′ may be output as a calculation result of a parameter representing the shape of the toroidal surface to be evaluated.

The figure which shows an example of the shape of a toroidal mirror. The figure for demonstrating an example of the shift | offset | difference of the shape of a toroidal mirror. The flowchart which shows the procedure of the toroidal surface evaluation method which is one Embodiment of this invention. A three-dimensional display example (a) of the difference between the actually measured value and the specification value of the shape of the concave toroidal mirror and a three-dimensional display example (b) of the difference between the same actually measured value and the provisional value that gives the minimum PV value.

Explanation of symbols

1 ... concave toroidal mirror 2 ... toroidal surface

Claims (3)

the measured obtaining a shape of the measured values of the toroidal surface and the shape measured by the three-dimensional measurement method of the contact or contactless a toroidal surface of a) evaluated,
Set the range of tolerance centered on the specifications of the parameters representing the shape of the toroidal surface of b) the evaluation as a change range of the provisional value of the parameter, while varying said tentative value within said alteration range, An optimization step of calculating a difference between the shape of the toroidal ideal surface calculated from the provisional value and the shape of the actual measurement value, and obtaining a provisional value that minimizes an evaluation value based on the difference;
c) an output step of outputting the temporary value finally obtained by the optimization step as a calculation result of the parameter;
Toroidal surface evaluation method including   2. The toroidal surface evaluation method according to claim 1, wherein the parameters are a curvature radius in the horizontal direction, a curvature radius in the vertical direction, a rotation of the shaft, and a tilt of the shaft, or the equivalent thereof. Characteristic toroidal surface evaluation method.   The toroidal surface evaluation method according to claim 1 or 2, wherein the evaluation value is either a PV value (difference between a maximum point and a minimum point) or an average value obtained by a least square method. Toroidal surface evaluation method.