JP4533158B2 - Image processing apparatus, image processing program, and refractive index distribution measuring apparatus - Google Patents

Description

  The present invention relates to an image processing apparatus and an image processing program for measuring an internal refractive index distribution of an object such as an optical element, and more particularly to an apparatus for measuring an internal refractive index distribution of an object by analyzing a transmitted wavefront. .

  In recent years, optical elements such as lenses used in digital cameras and laser beam printers are manufactured by molding optical glass and plastic, and optical elements having aspherical surfaces and free-form surfaces are also manufactured by molding. There are many. However, the molding can perform aspherical processing at a low cost, but a refractive index distribution is generated inside the optical element due to molding time and molding pressure at the time of manufacturing. If a refractive index distribution exists, an optical element that requires high optical performance has a great influence on imaging performance and the like, and the design value cannot be satisfied. For these reasons, measurement of the refractive index distribution is an important issue, and highly accurate measurement is required.

  In general, as a method for measuring the refractive index distribution of an optical element, transmitted wavefront measurement using an interferometer is widely used. However, in the conventional method, the refractive index distribution of an optical element is integrated in the light transmission direction. Only a three-dimensional refractive index distribution is observed, and a three-dimensional refractive index distribution including a distribution in the light transmission direction cannot be obtained. In order to obtain a three-dimensional distribution, it is necessary to divide and measure the optical element as a test object by thinly cutting it, and it is difficult to measure with high accuracy.

  In order to solve this problem, Patent Document 1 describes that a test object is immersed in a matching oil having substantially the same refractive index, and the test object is rotated around an axis orthogonal to the optical axis of the test wave. In addition, a method is disclosed in which the transmitted wavefront is measured one after another while the internal distribution is estimated in a cross-sectional shape of the wave to be detected by CT (computer tomography) analysis from the transmitted wavefront data.

As a method for further improving accuracy, Patent Document 2 discloses that a matching water tank is provided around the matching tank to circulate water at a constant temperature, and the outside is covered with a heat insulating material to reduce heat exchange with the outside. A method has been devised in which the temperature of the matching liquid is homogenized to reduce the influence of the temperature fluctuation of the matching liquid on the measured transmitted wavefront.
Japanese Patent No. 3423486 (paragraphs 0019-0039, FIGS. 1-3, etc.) JP-A-10-206281 (paragraphs 0024 to 0028, FIG. 1, etc.)

  However, with these methods, the temperature of the matching liquid at the time of measurement cannot be completely homogenized, and the influence of the background due to the temperature fluctuation of the matching liquid occurs, and this is accompanied by an output refractive index. The accuracy of the distribution data may be reduced.

  Furthermore, even if the temperature of the matching liquid can be completely homogenized, the boundary between the matching liquid and the test object in the measured transmitted wavefront becomes less clear as the surface refractive index difference between the matching liquid and the test object decreases. As a result, the boundary of the output internal refractive index distribution becomes unclear. Therefore, there is a possibility that it is not clear which part corresponds to the internal refractive index distribution of the test object.

  Therefore, the present invention makes it possible to generate the three-dimensional refractive index distribution data of an object placed in the matching liquid with high accuracy while suppressing the influence of the background due to the temperature fluctuation of the matching liquid. It is an exemplary object to provide an image processing apparatus, an image processing program, and a refractive index distribution measuring apparatus that can clearly generate a boundary of a refractive index distribution.

  In order to achieve the above object, the present invention as one aspect uses a first transmitted wavefront image obtained by irradiating an object in a liquid with light from a plurality of directions, and refraction inside the object. An image processing apparatus (image processing program) for generating refractive index distribution data representing a refractive index distribution, using shape data representing a three-dimensional shape of the object, by light transmitted through a liquid from a first transmitted wavefront image A correction unit (correction step) that generates a second transmitted wavefront image from which the transmitted wavefront component has been removed, and a refractive index distribution generation unit (refractive index distribution generator) that obtains the refractive index distribution data based on the second transmitted wavefront image Step).

  According to the present invention, three-dimensional refractive index distribution data of an object is obtained from temperature fluctuations of the liquid from a transmitted wavefront image measured by irradiating light from a plurality of directions to the object arranged in the liquid. It is possible to reduce the influence of the background due to, for example, with high accuracy, and to clearly generate the boundary.

  Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings.

  In the image processing apparatus and the image processing program of the present embodiment, the test object (object) is measured using transmission wavefront data (hereinafter referred to as a measurement transmission wavefront or a measurement transmission wavefront image) measured in a plurality of light beam directions. Internal refractive index distribution data (hereinafter simply referred to as refractive index distribution) is generated.

FIG. 1 shows a configuration example of a refractive index distribution measuring apparatus 100 including an image processing apparatus and an interferometer of the present embodiment. The refractive index distribution measuring apparatus 100 includes an interferometer 110 and an image processing apparatus 200. The image processing apparatus 200 includes a transmitted wavefront generation unit 120, a transmitted wavefront correction unit 130 , a refractive index distribution generation unit 140, and a refractive index distribution recording unit 160. In addition, the refractive index distribution generation unit 140 includes a simulation unit, a comparison unit, a penalty calculation unit, a change unit, and a shape extraction unit 150.

  The transmitted wavefront generating unit 120, the transmitted wavefront correcting unit 130, and the refractive index distribution generating unit 140 are configured by separate personal computers, and each component configuring the interferometer 110 and the image processing apparatus 200 includes a bus interface or the like. It is configured to be able to exchange data with each other. However, the entire image processing apparatus 200 or constituent parts other than the refractive index distribution generating unit 140 may be configured by a single computer, and each constituent part may function as a computer program. The extraction unit 150 may be configured by a separate computer.

  Further, in this embodiment, a refractive index distribution measuring device including the interferometer 110 and the transmitted wavefront generating unit 120 as components will be described. However, the interferometer 110 and the transmitted wavefront generating unit 120 are different from the refractive index distribution measuring device. The refractive index distribution measuring device may be configured as a device that only performs conversion from the transmitted wavefront to the refractive index distribution.

  In this case, the transmitted wavefront obtained and processed by the interferometer and the transmitted wavefront generation unit, which is a separate device from the refractive index distribution measuring apparatus, and stored in a recording medium such as a semiconductor memory or magnetic / optical disk is used to measure the refractive index distribution. You may make it possible to read (input) with an apparatus. Further, a configuration in which reading of a transmitted wavefront via such a recording medium and direct reading of a transmitted wavefront from the interferometer 110 and the transmitted wavefront generation unit 120 may be used in combination.

Further, in this embodiment, a refractive index distribution measuring device including the refractive index distribution recording unit 160 as a component will be described. However, the refractive index distribution recording unit 160 may be a device different from the refractive index distribution measuring device. .

The interferometer 110 can observe interference fringes in a plurality of different light beam directions (in other words, interference fringes formed by irradiating light from each direction in a plurality of directions) with respect to the test object O such as a lens. It is configured as follows. For example, as shown in FIG. 2, the interferometer 110 includes a laser light source 101 that emits coherent light, a beam expander 102 that expands the diameter of the laser light, and a beam splitter that divides the laser light into transmitted light and reference light. 103, a piezo mirror 104 that changes the optical path length of the reference light in the sub-wavelength order, a matching rod 105 that houses the test object O immersed in the matching liquid, and a direction of the test object O in the matching kit 105 is changed. A rotating mechanism 106, a reflecting mirror 107 that reflects the transmitted light that has passed through the test object O, a beam splitter 108 that superimposes the transmitted light and the reference light, and an image of interference fringes formed by the superimposed light This is a so-called two-beam interferometer configured by the imaging device 109 that captures images.

  In addition, although the test object O for description is also shown by FIG. 2, this test object O is not a component of this apparatus.

  The laser light emitted from the laser light source 101 is enlarged to a diameter that includes the test object O by the beam expander 102, and is transmitted through the test object O and transmitted light toward the test object O by entering the beam splitter 103. Without being divided into transmitted light that reaches the imaging device 109. The transmitted light divided by the beam splitter 103 passes through the matching rod 105 containing the test object O and enters the beam splitter 108 via the reflecting mirror 107. Further, the reference light divided by the beam splitter 103 is reflected by the piezo mirror 104 without passing through the test object O (is not transmitted), and enters the beam splitter 108. The transmitted light and the reference light incident on the beam splitter 108 are superimposed by the beam splitter 108. The superimposed laser light is incident on the imaging device 109. The imaging device 109 records (captures) an interference fringe image that is an image corresponding to the cross-sectional intensity of incident light.

  In measuring interference fringes, the test object O is placed on the rotating mechanism 106 in the matching bowl 105, and the inside of the matching bowl 105 is filled with a liquid (matching liquid) having a refractive index substantially equal to that of the test object O. Then, by rotating the rotation mechanism 106 to change the direction of the test object O, light is incident on the test object O from a plurality of directions, and interference fringes in each of the plurality of light beam directions are formed. Take a picture.

  The light incident / exit portion of the matching rod 105 is configured by arranging transparent flat plates in parallel. Since the inside of the matching bowl 105 is filled with a matching liquid having a refractive index substantially equal to that of the test object O, the transmitted light passes through the matching bowl 105 without being refracted. However, when there is a fluctuation (non-uniformity) in the refractive index inside the test object O, this is integrated in the light beam direction as a difference in optical path length, resulting in disturbance of the wavefront of the light emitted from the matching rod 105. When the transmitted light having this disturbance is superimposed on the reference light, an interference fringe corresponding to the cross-sectional intensity of the superimposed light appears, and the interference fringe is photographed by the imaging device 109. The captured image is output as measurement interference fringe data.

  The transmitted wavefront generation unit 120 generates a measured transmitted wavefront (first transmitted wavefront image) by image processing for each light beam direction from measurement interference fringe data (hereinafter simply referred to as measurement interference fringes) measured by the interferometer 110. . The image processing performed at this time will be described later, but an existing processing method for interference fringe analysis may be used.

  The transmitted wavefront correction unit 130 removes background noise due to temperature fluctuations of the matching liquid from the measured transmitted wavefront generated by the transmitted wavefront generation unit 120 using the shape data of the test object O. This detailed method will be described later.

  The refractive index distribution generation unit 140 collectively processes the measured transmission wavefronts for each light direction generated by the transmission wavefront generation unit 120 to generate a refractive index distribution (refractive index distribution data) inside the test object O. This refractive index distribution is three-dimensional volume data indicating what kind of refractive index distribution is present inside the test object O, and it is assumed that the test object O has such a refractive index distribution. The error between the estimated transmitted wavefront and the measured transmitted wavefront that is estimated to be obtained when the same measurement as that of 110 is performed is minimal and has a natural (that is, continuous) distribution. A method for generating such an internal refractive index distribution will be described in detail later.

  The shape extraction unit 150 is associated with the refractive index distribution generation unit 140, and by using the shape data of the test object O, the accuracy of the refractive index distribution generation and the generated test object O of the refractive index distribution are obtained. Improves consistency with the shape. Details of this will also be described later.

  The refractive index distribution recording unit 160 stores the refractive index distribution generated by the refractive index distribution generating unit 140 in the various recording media described above. The stored refractive index distribution can be used for optical design and molding evaluation.

  Hereinafter, a more detailed configuration and operation of each component of the refractive index distribution measuring apparatus 100 will be described.

In the interference fringe measurement, the piezo mirror 104 is driven with respect to one rotation position R _i of the rotation mechanism 106 with the test object O placed on the rotation mechanism 106 of the interferometer 110, and a plurality of reference light phases are detected. The interference fringe at θ _ij is imaged by the imaging device 109. The number of reference light phases used for one rotation position R _i depends on the processing method of the transmitted wavefront generation unit 120, but in this example, four reference light phases {θ _i1 for any rotation position. , Θ _i2 , θ _i3 , θ _i4 ,} = {0, π / 2, π, −π / 2}.

When photographing at four reference light phases is completed for a certain rotation position R _i , the rotation mechanism 106 is operated to set the subject O to another rotation position R _{i + 1} , and similarly photographing at four reference light phases. I do. The number of rotational positions at which the image is taken depends on the resolution and accuracy of the refractive index distribution that is finally required.

Note that the rotation mechanism 106 preferably includes a plurality of rotation axes such as a rotation axis and a pitch axis as shown in FIG. 14, and the rotation position R _i is not a single rotation angle, but a three-dimensional shape such as a quaternion. Described in rotation angle. A series of rotational positions {R _i } is set to have various rotational angles around each axis.

The measurement interference fringe F photographed in this way uses each rotation position R _i and reference light phase θ _ij ,
F (R _i , θ _ij , x, y)
Can be expressed as Note that x and y are coordinates on the image plane. FIG. 7 shows an interference fringe image in a certain light beam direction. When a refractive index distribution is generated in the portion of the test object O, the interference fringe is observed. The measured measurement fringe F is input to the transmitted wavefront generation unit 120.

The transmitted wavefront generation unit 120 receives the measurement interference fringes F (R _i , θ _ij , x, y) from the interferometer 110 and calculates the measured transmitted wavefronts F (R _i , x, y) at the respective rotational positions R _i . . The processing here is divided into a phase generation step S121 and a phase connection step S122, as shown in the flowchart of FIG.

  Here, each operation step in the refractive index distribution generation unit 140 including the transmission wavefront generation unit 120, the transmission wavefront correction unit 130, and the shape extraction unit 150 is executed by a computer program, but each step is regarded as a section. Accordingly, the refractive index distribution generation unit 140 including the transmission wavefront generation unit 120, the transmission wavefront correction unit 130, and the shape extraction unit 150 functions as an image processing apparatus including the above-described units. Further, when the refractive index distribution generation unit 140 including the transmission wavefront generation unit 120, the transmission wavefront correction unit 130, and the shape extraction unit 150 is executed as a computer program, all of these may be executed on a single computer.

First, a group of images having different reference light phases θ _{ij at} each rotational position R _i is extracted. In this example,
{Θ _i1 , θ _i2 , θ _i3 , θ _i4 ,} = {0, π / 2, π, −π / 2}
Images {F ₁ = F (R _i , 0, x, y), F ₂ = F (R _i , π / 2, x, y), F ₃ = F (R _i , π, x, y) ), F ₄ = F (R _i , −π / 2, x, y)}
In the phase generation step S121, the following equation is obtained from these group of images:

By
−π ≦ I ′ (Ri, θi _j , x, y) <π
An unconnected phase image I ′ (Ri, θi _j , x, y) is generated. In the above formula, the range of tan ⁻¹ is (0, π).

If the standard deviation of the measurement error expected in the interference fringe image F is a constant value σ _F , the standard deviation σ _{I ′} of the error of _{I ′} is

Therefore, when the transmitted light is weak, or in pixels where F ₂ and F ₄ or F ₁ and F ₃ are close to each other due to noise of the imaging device 109, σ _{I ′} may become very large.

In the unconnected phase image I ′ obtained in this way, the phase may fluctuate from the vicinity of + π to the vicinity of −π in the adjacent pixels even for the portion that is originally continuously changing. Such a phenomenon is called wrapping. Therefore, in the next phase connection step S122, phase connection (unwrap) is performed to solve this. In the phase connection, it is a difference in the value of the unconnected phase image I ′ between _two adjacent pixels (x ₁ , y ₁ ) and (x ₂ , y ₂ ) in the interference fringe image.
| I ′ (R _i , x1, y1) −I ′ (R _i , x ₂ , y ₂ ) |
When is larger than π, 2nπ (n is an integer) is added to or subtracted from one image to adjust the phase difference between adjacent pixels to be π or less. At this time, the zero point is set in a region where the test object O is not shown in the image.

  The transmitted wavefront generation unit 120 sets the image adjusted in this way as a measured transmitted wavefront image I (Ri, x, y), and inputs it to the transmitted wavefront correction unit 130.

  FIG. 8 shows a measured transmitted wavefront image in a certain ray direction. The area a in the figure is the background area of the matching liquid only. In addition, the region b is a test object region where the test object O exists, and an image with gradation is applied due to the phase difference of light transmitted through the background region.

  In the transmitted wavefront generation unit 120, a region where the measured transmitted wavefront image I cannot be appropriately determined may occur due to noise on the measurement interference fringe F, excessive interference fringes, or shadows of the rotation mechanism 106. These areas are not filled with wavefront values obtained by interpolation from the surroundings, and the areas are indefinite in the transmitted wavefront correction unit 130 by setting the wavefront value to “not a number” (NaN). To be notified.

  In the transmitted wavefront correction unit 130, the background noise or the like due to the matching liquid is detected from the measured transmitted wavefront image I (Ri, x, y) received from the transmitted wavefront generation unit 120 in the optical path direction (light beam) of the object O at each rotation angle. The corrected transmission wavefront image Ic (Ri, x, y) is output as a second transmitted wavefront image. The operation of the transmitted wavefront correction unit 130 will be described with reference to the flowchart of FIG.

  The process of the transmitted wavefront correction unit 130 includes a test object shape generation step S131, a test object transmission shape generation step S132, a background extraction step S133, an interpolation step S134, and a thickness consideration step S135. .

  First, in the test object shape generation step S131, three-dimensional shape data of the test object O is generated from CAD data in which the inside of the test object shape is 1 and the others are 0. This method is effective when data from CAD can be used. Further, such three-dimensional shape data may be input from another device.

  In the test object transmission shape generation step S132, the coordinates of the three-dimensional shape data of the test object O obtained by the above method as shown in FIG. v, w). Furthermore, when the three-dimensional shape data is a function G (u, v, w), the shape data of the test object O at the rotation angle θi is integrated in the optical path direction according to the following equation.

  Here, Rot (Ri) is a three-dimensional rotation matrix representing the rotation position Ri, and is fixed to the interferometer 110 from the orthogonal coordinate system (u, v, w) fixed to the test object O. The transformation to the coordinate system (x, y, z) is shown.

  In this integration, the thickness data D (Ri, x, y) in the optical path direction of the shape of the test object at each rotational position can be obtained by multiplying the size d [mm] of one voxel.

D (Ri, x, y) = M (Ri, x, y) × d
For example, in the thickness data D (Ri, x, y),
D (Ri, x, y)> 0
, That is, when the other part is set to 1, a silhouette image (transmission shape image) in the optical path direction of the test object shape at each rotational position as shown in FIG. A specimen transmission shape image M (Ri, x, y) to be expressed is obtained. Here, the region b is a silhouette image region of the test object.

  In the background extraction step S133, the transmitted wavefront image I (Ri, x, y) and the test object transmission shape image M (Ri, x, y) are multiplied to obtain the transmitted wavefront image I (Ri, x, y). ), The image is extracted so that the value of the test object portion is 0 and the other background regions have values other than 0, and the image is extracted as a background image B (Ri, x) as shown in FIG. , Y) (first liquid transmission wavefront image). In FIG. 11, a region is a background region having a value, b region is a test object region, and a value is 0 region. That is, the background image B represents a transmitted wavefront component due to light transmitted through the matching liquid.

  In the interpolation step S134, in the background image B (Ri, x, y) obtained in the background extraction step S133, almost all of the background is due to the matching liquid in the matching tank 105, and the refractive index is further increased. Assuming that there is a smooth change, by interpolating the value of the specimen region where the value is set to 0 from the value of the area other than the specimen area, there is no specimen, that is, the specimen A background image B ′ (Ri, x, y) (second liquid transmitted wavefront image) representing the transmitted wavefront of the entire region when the inspection region is filled with the matching liquid is estimated. The background image B ′ (Ri, x, y) obtained in this way has a background value in which the test object region b surrounded by the dotted line is estimated as shown in FIG.

  In the thickness consideration step S135, in the background image B ′ (Ri, x, y) obtained in the interpolation step S134, the transmission distance of the matching liquid is shortened by placing the test object in the matching tank 105, Correct the amount of background that decreases.

For this correction, the thickness data D (Ri, x, y) in the optical path direction of the test object shape at each rotational position obtained in the test object transmission shape generation step S132, the length L of the matching tank in the optical path direction, and From the background image B ′ (Ri, x, y) estimated in the interpolation step S134, assuming that the test object is not in the matching tank,
Bc (Ri, x, y) = B ′ (Ri, x, y) × {(LD) / L}
Thus, as shown in FIG. 13, the correction background image Bc (Ri, x, y) (third liquid transmission wavefront image) when the test object is present in the matching tank 105 is derived. In other words, the corrected background image Bc represents a transmitted wavefront component due to light transmitted through the matching liquid that overlaps the object region in each light beam direction.

  In FIG. 13, the background value of the region b is more accurate than the background image B ′ (Ri, x, y) of FIG. 12 by considering the thickness of the test object.

  The transmitted wavefront correction unit 130 takes the difference between the corrected background image Bc (Ri, x, y) thus obtained and the measured transmitted wavefront image I (Ri, x, y) and obtains the background from the matching liquid. A corrected transmitted wavefront image Ic (Ri, x, y) is generated. Then, the corrected transmitted wavefront image Ic (Ri, x, y) is input to the refractive index distribution generation unit 140.

  The refractive index distribution generation unit 140 corrects the transmitted wavefront image Ic (Ri, x, y) obtained from the measured transmitted wavefront image I (Ri, x, y) of the test object O measured in a plurality of light beam directions in this way. y) is used to estimate the three-dimensional refractive index distribution N (u, v, w) in the test object O.

  The operation of the refractive index distribution generation unit 140 will be described with reference to the flowchart of FIG. The processing of the refractive index distribution generation unit 140 includes an initial distribution generation step S141, a simulation (optical path length integration) step S142, a comparison step S143, a penalty calculation step S144, a correction (change) step S145, and a shape extraction step S146. And a convergence determination step S147 and an output step S148. Among these, an iterative loop is formed from the optical path length integration step S142 to the convergence determination step S147, and is repeated a plurality of times.

  Further, the refractive index distribution generation unit 140 receives, as input data, the corrected transmitted wavefront image I (Ri, x, y) group and the rotation position Ri when each transmitted wavefront is acquired, and the estimated refractive index distribution N (u , V, w).

First, in the initial distribution generation step S141, an initial distribution N ⁰ of the estimated refractive index distribution N ⁿ (first refractive index distribution data) is generated. Here, the estimated refractive index distribution N ⁿ is a voxel expression representing the refractive index of each portion obtained by dividing the (u, v, w) space, for example, every 1 mm. The initial estimated refractive index distribution N ⁰ generated in this step does not affect the finally generated output refractive index distribution, and thus may be any refractive index distribution. For example, it is a uniform value.
N ⁰ (u, v, w) = 0
And

In the simulation step S142, an estimated transmitted wavefront image I ⁿ (third transmitted wavefront image) that will be obtained when the estimated refractive index distribution N ⁿ is the refractive index distribution N of the test object O. Is generated. For that purpose, considering the rotational position R _i at the time of interference fringe measurement, that is, the direction of the light beam,
I ⁿ (R _i , x, y) = ∫N ⁿ {u (R _i , x, y, z), v (R _i , x, y, z), w (R _i , x, y, z) } Dz (3)
And That is, (in other words, the optical path direction) the light beam direction by Equation (3) by integrating the estimated refractive index distribution N ⁿ in, it calculates the estimated transmitted wavefront image I ^n.

Note that this is expressed as a determinant I ⁿ = AN ⁿ by using a vector representation of N ⁿ and I ⁿ . A is a system matrix representing projective transformation. Replaced the vector ^{representation, N n (u, v,} w) and ^{I n (Ri, x, y} ) of the one-dimensional vector _{^{{N n u, v, w}} } and _{^{{I n Ri, x, y}} } and It is a thing.

In the comparison step S143, actual interferometer 110 and the estimated transmitted wavefront image ^{I n} obtained in the simulation step S142, the correction obtained by the transmitted wavefront generation unit 120 and the transmitting wave front correction unit 130 transmitted wavefront image Ic (second transparent Wavefront image), and the difference between these,
d ⁿ (R _i , x, y) = I ⁿ (R _i , x, y) −Ic (R _i , x, y)
Is input to the correction step S145 as an estimation error (first information). Incidentally, with respect to the region where the wavefront value has not been determined appropriately among the corrected transmitted wavefront image Ic, and 0 the value of the corresponding region of the d ^n.

On the other hand, in the penalty calculation step S144, a minute correction amount {δN ⁿ | P (N ⁿ + δN ⁿ )> P (N ⁿ )} that increases the penalty function P (N ⁿ ) defined for the estimated refractive index distribution. 2nd information) is calculated, and it inputs into correction step S145.

This penalty function represents “unnaturalness” (or discontinuity) of the refractive index distribution N ⁿ . For example, the refractive index distribution is considered as a continuous distribution, and the penalty function P (N ⁿ ) is the square norm of the N ⁿ spatial variation ∇N ⁿ .
P (N ⁿ ) = (∇N ⁿ ) ²
And its slope is
δN ⁿ = ∇P (N ⁿ ) = ΔN ⁿ
And If this is expressed in a discrete system,
P (N ⁿ )
= (∇N ⁿ ) ²
= Σ _{u, v, w} N ⁿ (u, v, w) {6N ⁿ (u, v, w) −N ⁿ (u + 1, v, w) −N ⁿ (u−1, v, w)
−N ⁿ (u, v + 1, w) −N ⁿ (u, v−1, w) −N ⁿ (u, v, w + 1) −N ⁿ (u, v, w−1)}
δN ⁿ
= ΔN ⁿ
= Σ _{u, v, w} 2 {6N ⁿ (u, v, w) −N ⁿ (u + 1, v, w) −N ⁿ (u−1, v, w)
−N ⁿ (u, v + 1, w) −N ⁿ (u, v−1, w) −N ⁿ (u, v, w + 1) −N ⁿ (u, v, w−1)}
The part (u, v, w) and its neighboring parts (u, v, w), (u + 1, v, w), (u-1, v, w), (u, v + 1, w), A partial penalty calculated depending only on the refractive index N of (u, v-1, w), (u, v, w + 1), (u, v, w-1),
p (u, v, w)
= N ⁿ (u, v, w) {6N ⁿ (u, v, w) −N ⁿ (u + 1, v, w) −N ⁿ (u−1, v, w)
−N ⁿ (u, v + 1, w) −N ⁿ (u, v−1, w) −N ⁿ (u, v, w + 1) −N ⁿ (u, v, w−1)}
The penalty is the sum of them,
P (N ⁿ ) = Σ _{u, v, w} p (u, v, w)
It is expressed.

In modified step S145, on the basis of the fine correction amount .delta.N ⁿ obtained in the estimated error ^{d n} and penalty calculation step S144 obtained in the comparison step S143, it modifies the estimated refractive index distribution ^{N n} (changed). To this end, first, the difference d ⁿ (Ri, x, y) on the transmitted wavefront image space (R _i , x, y) obtained in the comparison step S143 is used as the standard deviation σ _I ( R _i, x, divided by y), further test object coordinate space (u, v, w) on the value ^e n (u, v, into a w). This is a conversion from the estimated refractive index distribution N ⁿ to the estimated transmitted wavefront image I ⁿ in the simulation step S142. I ⁿ = AN ⁿ
It is a reverse projection represented by the following formula (4).

It utilizes a vector representation of d ⁿ and e ^n, the determinant,
e ⁿ = A ^t d ⁿ
Can be described. Depth is the distance that the transmitted light measured as the measured transmitted wavefront image I (R _i , θ, x, y) at the time of interference fringe measurement crosses the object O, but it is not necessarily an accurate value. Instead, a typical value or a typical thickness of the test object may be set to a constant value. And the estimated refractive index distribution N is
^{N n + 1 = N n +} μ (e n -βδN n)
To obtain a new estimated refractive index distribution N ^{n + 1} (second refractive index distribution data). Note that μ in the above equation is a parameter indicating the step length of successive approximation,
0 <μ / σ _I (R _i , x, y) <2
Takes the value of

In the shape extraction step S146 (shape extraction unit 150), the three-dimensional shape data of the test object O acquired from the CAD data in the transmitted wavefront correction unit 130 from the estimated refractive index distribution N ^{n + 1} obtained in the correction step S145. Then, the refractive index distribution only inside the shape of the test object is extracted, and the estimated refractive index distribution after the shape extraction is obtained. For example, a function G (u, v, w) in which the object shape portion is 1 and the other portion is 0 is obtained from the three-dimensional shape data,
N ^{n + 1} = N ^{n + 1} × G (u, v, w)
By calculating the above, the refractive index distribution only inside the object shape is extracted.

  In convergence determination step S147, it is determined whether successive approximation has converged. If it has converged, the process proceeds to output step S148. If it has not converged, the process proceeds to simulation step S142 and penalty calculation step S144. In the case of unconvergence, the estimated refractive index distribution input to the simulation step S142 and the penalty calculation step S144 is the estimated refractive index distribution after shape extraction generated by the calculation in the shape extraction step S146.

Convergence as the determination method, the correction amount of the norm beta in the modified Step S145 ^{| e n} -βδN n ^| or if falls below a predetermined threshold, the previous correction amount norm ^{β | e n-1 -βδN n} -1 | It is better to exceed the above. In addition to this, it may be considered that the predetermined number of iterations has converged when the predetermined number of times has been reached or the processing time has reached a predetermined time.

  In this iterative loop, the estimated refractive index distribution N is changed by the correction step S145, and each time the estimated error d and the penalty P (N) are evaluated,

Changes to N which becomes smaller.

In the output step S148, and outputs the estimated refractive index distribution N ^m at that time as the generation value of the refractive index generation unit 140 (output refractive index distribution data) N. This final refractive index distribution N is

  To minimize N.

Note that N output from the refractive index distribution generation unit 140 is a relative value of the amount of phase change per unit length with respect to the matching liquid, so that this can be converted to a standard unit refractive index. , Λ is the wavelength of the laser beam, N ₀ is the refractive index of the matching liquid,

And

The refractive index distribution recording unit 160 records the refractive index distribution N generated by the refractive index distribution generating unit 140. As an output expression format, the refractive index N (u, v, w) of each voxel may be enumerated, or a polynomial approximation.
N (u, v, w) ≈A ₀ + A ₁ u + A ₂ v + A ₃ w + A ₄ u ² + A ₅ v ² + A ₆ w ²
+ A ₇ uv + A ₈ vw + A ₉ wu + (8)
May be enumerated as the approximation coefficients a _i . Moreover, you may enumerate as a fitting coefficient in fitting functions, such as a Fourier series and a zernik polynomial.

  As described above, according to the present embodiment, by using the shape data of the test object O for the refractive index distribution measurement, the transmitted wavefront correction unit 130 removes the influence of the background of the measured transmitted wavefront. Thus, it is possible to perform an iterative simulation process in the refractive index distribution generation unit 140 while extracting the shape of the test object in the shape extraction unit 150. Therefore, the final refractive index distribution N with high definition and less noise can be generated from the transmitted wavefront measured from a plurality of light beam directions.

  More specifically, the image processing apparatus 200 according to the present embodiment uses the shape data of the test object O to transmit the test object O in order to correct the measured transmission wavefront having a large influence of the measured background. Obtain the shape and divide the measured transmission wavefront into the part of the test object and the other part, and the temperature fluctuation of the matching liquid when there is no test object from the transmitted wavefront outside the transmission shape of the test object The background due to is estimated by interpolation. Then, by subtracting the estimated background from the measured transmitted wavefront, the background component due to temperature fluctuation of the matching liquid in the formulated transmitted wavefront can be corrected.

  Furthermore, the background component in the measured transmitted wavefront is estimated by subtracting this estimated background from the measured transmitted wavefront by estimating the background less by the thickness of the measured object from the background in consideration of the thickness of the measured object. Can be corrected more accurately.

  And by using this corrected measurement transmission wavefront, the inaccuracy of the measurement transmission wavefront due to the background and noise is reduced, and the measurement accuracy of the internal refractive index distribution of the test object O can be improved. .

  (

  The image processing method of the first embodiment described above can also be applied to a known CT method, that is, a refractive index distribution measurement method using Fourier transform.

  FIG. 15 shows a configuration example of the refractive index distribution measuring apparatus 100 ′ of the present embodiment. The refractive index distribution measuring apparatus 100 ′ is configured by an interferometer 110 and an image processing apparatus 200 ′. The image processing apparatus 200 ′ includes a transmitted wavefront generation unit 120, a transmitted wavefront correction unit 130, and a refractive index distribution generation unit. 140 ′, a shape extraction unit 150 ′, and a refractive index distribution recording unit 160. Each of these components is configured to be able to exchange data with each other via a bus interface, for example.

  The interferometer 110, the transmitted wavefront generation unit 120, the transmitted wavefront correction unit 130, and the refractive index distribution recording unit 160 are the same as those in the first embodiment, but the refractive index distribution generation unit 140 ′ in the present embodiment uses Fourier transform. The refractive index distribution data is generated, and the shape extraction unit 150 ′ extracts the shape of the test object in the generated refractive index distribution.

  Here, also in the present embodiment, as in the first embodiment, each operation step in the refractive index distribution generating section 140 ′ including the transmitted wavefront generating section 120, the transmitted wavefront correcting section 130, and the shape extracting section 150 ′ is performed by a computer. Although executed by the program, by regarding each step as a section, the refractive index distribution generation unit 140 ′ including the transmission wavefront generation unit 120, the transmission wavefront correction unit 130, and the shape extraction unit 150 ′ includes the above-described units. It functions as an image processing device. Further, when the refractive index distribution generation unit 140 ′ including the transmission wavefront generation unit 120, the transmission wavefront correction unit 130, and the shape extraction unit 150 ′ is executed as a computer program, all of these may be executed on a single computer. Good.

  Hereinafter, a more detailed operation of each component of the refractive index distribution measuring apparatus 100 ′ will be described.

  From the interference fringe measurement to the transmitted wavefront generation processing, as in the first embodiment, the measurement interference fringe image F (Ri, x, y) is obtained using the interferometer 110, and is input to the transmitted wavefront generation unit 120 for transmission. The wavefront generation unit 120 generates a transmitted wavefront image I (Ri, x, y). The transmitted wavefront image I (Ri, x, y) is input to the transmitted wavefront correction unit 130.

  The transmitted wavefront correction unit 130 is substantially the same as in the first embodiment. However, when obtaining the shape data of the three-dimensional test object O in the test object shape generation step S131, if the shape is not complicated, from the drawing Shape data may be generated by obtaining a dimension and creating a function. For example, in the case where the test object O is a coaxial spherical lens, the diameter, thickness, radius of curvature of each surface, etc. are input using a spherical function, and the orthogonality fixed to the test object O is input. Three-dimensional shape data on coordinates (u, v, w) is generated. The generated three-dimensional shape data is, for example, a function G (u, v, w) in which the object shape portion is 1 and the other portions are 0. Then, the corrected transmitted wavefront image Ic (Ri, x, y) is applied to the generated three-dimensional shape data function G (u, v, w) by performing the same process as the transmitted wavefront correction unit 130 of the first embodiment. ) And input to the refractive index distribution generator 140 ′.

In the refractive index distribution generation unit 140 ′, the corrected transmitted wavefront image Ic (Ri, x, y) of the test object O measured in a plurality of light beam directions obtained in this way is obtained for each y _j by Icy _j ( Two-dimensional Fourier transform in the x direction is performed as x, R). Further, a two-dimensional refractive index distribution in y _j is generated by performing a two-dimensional inverse Fourier transform by converting the polar coordinates (r, φ) to the orthogonal coordinates (u, v).

next,
u = rcosφ, v = rsinφ, w = y
N (rcosφ, rsinφ) = ∫Ic (x, Ri) exp (−irx) dx
Is repeated for each y _j to generate a three-dimensional refractive index distribution N (u, v, w) and input it to the shape extraction unit 150 ′.

  Here, the obtained refractive index distribution N (u, v, w) includes the refractive index distribution of the test object O and the surrounding matching liquid portion, and the boundary of the test object shape becomes unclear, and the test object The refractive index distribution inside the specimen is not clear.

Therefore, the shape extraction unit 150 ′ uses the refractive index distribution N (u, v, w) obtained by the refractive index distribution generation unit 140 ′ and the object shape generation step S131 obtained by the transmitted wavefront correction unit 130. A three-dimensional shape data function G (u, v, w) of the inspection object O,
N ′ (u, v, w) = N (u, v, w) × G (u, v, w)
Thus, the refractive index distribution N ′ (u, v, w) of the object shape portion is taken out. The obtained refractive index distribution N ′ (u, v, w) is input to the refractive index distribution recording unit 160 and recorded.

  Further, the explanation related to the penalty in each of the above embodiments will be supplemented. First, in Example 1, the correction amount calculated in the correction step can be 0 for the estimated refractive index distribution (first refractive index distribution data) where the penalty is an extreme value. The correction amount may be a penalty gradient. The correction amount can be a value that increases the penalty by adding to the estimated refractive index distribution.

Further, as described in the first embodiment, the penalty can be expressed as a sum of partial penalties that can be calculated for each part of the estimated refractive index distribution, and the partial penalty depends only on the refractive index of the part and the vicinity thereof. Can be.
The penalty can be set such that the value increases as the non-uniformity of the refractive index distribution represented by the first refractive index distribution data increases. The penalty can also include a term that is positively correlated with the difference between the estimated refractive index distribution and its smoothed distribution. Furthermore, the penalty can be positively correlated with the amount of high frequency components in the estimated refractive index distribution).

  Further, as described in the first embodiment, the refractive index distribution may be expressed as a coefficient of a polynomial in addition to the refractive index output of each part of the glass material.

1 is a block diagram showing a configuration of a refractive index distribution measuring apparatus that is Embodiment 1 of the present invention. FIG. 3 is a diagram illustrating a configuration of an interferometer used in the refractive index distribution measuring apparatus according to the first embodiment. FIG. 5 is a diagram illustrating processing of a shape extraction unit in the refractive index distribution measurement apparatus according to the first embodiment. 6 is a flowchart showing an operation of a transmitted wavefront generating unit in the refractive index distribution measuring apparatus according to the first embodiment. 6 is a flowchart showing an operation of a transmitted wavefront correction unit in the refractive index distribution measuring apparatus according to the first embodiment. 5 is a flowchart showing an operation of a refractive index distribution generation unit in the refractive index distribution measuring apparatus according to the first embodiment. Explanatory drawing which shows the example of an interference fringe. Explanatory drawing which shows the example of a transmitted wave front. Explanatory drawing which shows the example of the three-dimensional shape of a test object. Explanatory drawing which shows the example of the permeation | transmission shape of a test object. Explanatory drawing which shows the example of a background image. Explanatory drawing which shows the example of an interpolation background image. Explanatory drawing which shows the example of the correction | amendment background image which performed thickness correction of the to-be-tested object. Explanatory drawing which shows the example of the rotation mechanism in an interferometer. The block diagram which shows the structure of the refractive index distribution measuring apparatus which is Example 2 of this invention. FIG. 10 is a diagram illustrating processing of a shape extraction unit in the refractive index distribution measuring apparatus according to the second embodiment.

Explanation of symbols

DESCRIPTION OF SYMBOLS 100,100 'Refractive index distribution measuring apparatus 105 Matching rod 109 Imaging apparatus 110 Interferometer 120 Transmission wavefront generation part 130 Transmission wavefront correction part 140 Refractive index distribution generation part 150 Shape extraction part 160 Refractive index distribution recording part 200,200' Image processing apparatus

Claims (13)

An image processing apparatus for generating refractive index distribution data representing a refractive index distribution inside an object using first transmitted wavefront images respectively measured by irradiating light from a plurality of directions to the object in the liquid,
A correction unit that generates a second transmitted wavefront image obtained by removing a transmitted wavefront component of light transmitted through the liquid from the first transmitted wavefront image, using shape data representing a three-dimensional shape of the object;
An image processing apparatus comprising: a refractive index distribution generation unit that obtains the refractive index distribution data based on the second transmitted wavefront image. The correction unit is
Using the shape data, generate a transmission shape image representing the shape of the object in each direction,
Generating a liquid transmission wavefront image representing a transmission wavefront component of light transmitted through the liquid based on the transmission shape image and the first transmission wavefront image;
The image processing apparatus according to claim 1, further comprising generating the second transmitted wavefront image based on the first transmitted wavefront image and the liquid transmitted wavefront image. The correction unit is
Using the shape data, generate a transmission shape image representing the shape of the object in each direction,
Based on the transmission shape image and the first transmission wavefront image, generate a first liquid transmission wavefront image representing a transmission wavefront component of light transmitted through the liquid region outside the object region in each direction,
Based on the first liquid transmission wavefront image, a second liquid transmission wavefront image in which a transmission wavefront component due to light transmitted through the liquid is estimated when the object region is filled with the liquid is generated. ,
The image processing apparatus according to claim 1, wherein the second transmitted wavefront image is generated based on the first transmitted wavefront image and the second liquid transmitted wavefront image. The correction unit is
Based on the second liquid transmitted wavefront image and the thickness information of the object in each direction, a third liquid transmitted wavefront representing a transmitted wavefront component due to light transmitted through the liquid overlapping the object region in each direction. Generate an image,
The image processing apparatus according to claim 3, wherein the second transmitted wavefront image is generated based on the first transmitted wavefront image and the third liquid transmitted wavefront image. The refractive index distribution generator is
A simulation unit that generates a third transmitted wavefront image by simulating the transmitted wavefront in each direction based on the first refractive index distribution data;
A comparison unit that compares the third transmitted wavefront image with the second transmitted wavefront image and generates first information indicating the comparison result;
A change unit that generates second refractive index distribution data by changing the first refractive index distribution data based on the first information,
Using the second refractive index distribution data as the first refractive index distribution data, the second refractive index distribution data generated by repeating the processing in each section is used as the refractive index representing the refractive index distribution inside the object. The image processing apparatus according to claim 1, wherein the image processing apparatus is distribution data.   The image processing apparatus according to claim 5, wherein the simulation unit generates the third transmitted wavefront image by integrating the first refractive index distribution data in each direction. Using the shape data, further comprising a shape extraction unit for extracting the refractive index distribution data of only the object from the second refractive index distribution data;
7. The image processing according to claim 5, wherein the processing in each of the units is repeated using, as the first refractive index distribution data, the refractive index distribution data of only the object in the second refractive index distribution data. 8. apparatus. A penalty calculating unit that generates second information used to change the first refractive index distribution data based on a penalty defined for the first refractive index distribution data;
The change unit generates the second refractive index distribution data by changing the first refractive index distribution data based on the first information and the second information. Item 8. The image processing apparatus according to any one of Items 1 to 7.   The second information is a change amount of the first refractive index distribution data, and is a value that increases the penalty by adding to the first refractive index distribution data. The image processing apparatus according to 8.   10. The image processing apparatus according to claim 8, wherein the penalty is a higher value as the nonuniformity of the refractive index distribution represented by the first refractive index distribution data is larger. An image processing apparatus according to any one of claims 1 to 10,
A refractive index distribution measuring apparatus comprising: an interferometer that acquires the first transmitted wavefront image. An image processing program for generating refractive index distribution data representing a refractive index distribution inside the object using first transmitted wavefront images measured by irradiating light from a plurality of directions to the object in the liquid,
On the computer,
Using the shape data representing the three-dimensional shape of the object, a correction step for generating a second transmitted wavefront image obtained by removing a transmitted wavefront component due to light transmitted through the liquid from the first transmitted wavefront image;
An image processing program for executing a refractive index distribution generation step for obtaining the refractive index distribution data based on the second transmitted wavefront image. The refractive index profile generation step includes
A simulation step of generating a third transmitted wavefront image by simulating the transmitted wavefront in each direction based on the first refractive index distribution data;
A comparison step of comparing the third transmitted wavefront image and the second transmitted wavefront image and generating first information indicating the comparison result;
Changing the first refractive index distribution data based on the first information to generate second refractive index distribution data,
Using the second refractive index distribution data as the first refractive index distribution data, the second refractive index distribution data generated by repeating the processing in each section is used as the refractive index representing the refractive index distribution inside the object. The image processing program according to claim 12, wherein the image processing program is distribution data.