WO2004003467A1

WO2004003467A1 - Phase-shifting diffraction grating interferometer and its measuring method

Info

Publication number: WO2004003467A1
Application number: PCT/KR2002/001331
Authority: WO
Inventors: Seung-Woo Kim; Tae-Joon Hwang
Original assignee: Korea Advanced Institute Of Science & Technology
Priority date: 2002-06-27
Filing date: 2002-07-15
Publication date: 2004-01-08
Also published as: KR100457656B1; AU2002319925A1; KR20040001098A

Abstract

Disclosed is a phase-shifting diffraction grating interferometer using diffraction grating. When a light source incident to the diffraction grating is resolved into several diffraction lights, one of them having a diffraction element is selected as a reference light, and other part having the diffraction element or another light having other diffraction element is selected as a light directing to an object to be measured. The light directing to the object to be measured is reflected from the object and is incident to the diffraction grating and then diffracted, and object lights made by the diffraction generates the reference light and an interference pattern. When the diffraction grating is moved in a longitudinal direction, the object light or the reference light is phase-shifted, a number of interference patterns are obtained, and the interference patterns are analyzed to obtain a shape of the measured object. The present invention relates to an improved diffraction grating interferometer capable of being used in an optical metrology field, and the interferometer includes interferometers of various types, which is capable of measuring various kinds of objects to be measured. The phase-shifting diffraction grating interferometer includes a light source part, a beam splitter or a light direction controller, a phase-shifting generator, an interference pattern generator, an interference pattern obtaining part, a central processing unit and a result displaying part. The light source part includes a light source and a lens, a pinhole, a collimator or an optical fiber. The optical elements can be removed according to characteristics of this system or replaced by other optical elements.

Description

PHASE-SHIFTING DIFFRACTION GRATING ITERFERQMETER AND

ITS MEASURING METHOD

Technical Field The present invention relates to a phase-shifting diffraction grating interferometer using a diffraction grating. Specifically, the present invention relates to a phase-shifting diffraction grating interferometer and measuring method therefore, which selects one diffraction component as a reference light if a light incident upon a diffraction grating from a light source is split into several lights, selects the other part of the one diffraction component or another diffraction component as a light directing to a measurement target object, enables an object light incident upon and then diffracted at the diffraction grating after being reflected at the measurement target object to generate an interference pattern together with the reference light, acquires a plurality of interference patterns by phase-shifting the object light or the reference light through movement of the diffraction grating along a longitudinal direction, and obtains a profile of the measurement target object by analyzing the interference patterns.

Background Art

Among techniques for measuring and evaluating surfaces of objects having any shape, and precise surfaces of optical elements, such as a mirror, a lens, a filter etc., a technique using light is most widely used. A Twyman- Green interferometer and a Fizeau interferometer are well known as interferometers for measuring the precise surface using light. A basic principle of the above interferometers is that one light is split into two lights by a beam splitter, one being used as a reference light and the other being used as an object light. The object light reflected at a measurement object interferes with the reference light, thus to obtain an interference pattern. Then, surface information of the measurement object is obtained by analyzing the interference pattern.

The Twyman-Green interferometer utilizes a glass plate of a specially coated plane form or a beam splitter with a cube form. However, it is extremely complicated to manufacture the beam splitter because its each surface should have flatness of high precision, and if necessary, non- reflective coating is demanded in order to prevent unnecessary reflection. Moreover, the Twyman-Green interferometer necessitates a reference mirror surface of high precision for relative comparison with a measurement surface. However, it is difficult to make the reference surface, and especially, it is almost impossible to manufacture a large-sized reference surface used to measure a large-sized measurement object.

A phase-shifting interferometer is widely used to obtain more accurate measurement results than the Twyman-Green interferometer. For the phase-shifting interferometer, there have been developed various types of optical configurations and corresponding algorithms according to measurement objects and measurement purposes (refer to " Optical Shop Testing" , second edition, Wiley, 1992, Chapter 14). A general phase- shifting method and principle are well known in the art and thus a description thereof will not be made herein.

A precisely fabricated beam splitter and a reference mirror with good flatness are necessary for an interferometer. However, the precise beam splitter and the reference mirror with good flatness are hard to manufacture and they are expensive, thereby raising the cost of equipment. While a large-sized reference mirror is needed in order to measure a large-sized measurement object, it is almost impossible to manufacture the large-sized reference mirror, apart from the manufacturing cost. A diffraction grating can be used as a beam splitter or a light ray path controller because a short wavelength light source incident upon the diffraction grating is diffracted in various directions. On the basis of a zero order diffraction light which is transmitted or reflected at an incident surface of light, a light diffracted at the nearest angle is represented by a first order diffraction light, a light diffracted at an angle of the second magnitude is represented by a second order diffraction light, a light diffracted at an angle of the third magnitude is represented by a third diffraction light, and a light diffracted at an angle of the n-th magnitude is represented by an n-th order diffraction light. Examples of the interferometer for separating one light into several lights by using the properties of the diffraction grating are disclosed in many papers (for instance, ' Optical Shop Testing" , second edition, wiley, 1992). A plane shape measurer similar to the Twyman-Green interferometer, using two different diffraction components has been proposed by C. R. Munnerlyn (refer to " A simple laser interferometer" , Appl. Opt. 8(4) 827-829, 1969, by C. R. Munnerlyn). In the proposed interferometer, a reflective type diffraction grating of a wide area is used as the beam splitter. A positive first order diffraction component and a negative first order diffraction component are used as a light directing to a measurement target object and a reference light, respectively. This interferometer is similar in form to the Twyman-Green interferometer but it is more similar in principle to the Fizeau interference. The proposed interferometer is very simple because the surface of the diffraction grating functions as the reference surface. However, since the diffraction grating of a very wide area corresponding to the measurement area is used as the beam splitter and the reference surface, a serious system error may occur in the case where the flatness of the diffraction grating is not good or the grating groove of the diffraction grating is not uniform. An interferometer for reducing a system error caused by the inhomogeneity or irregularity of the diffraction grating generated by using the diffraction grating of a very wide area has been proposed (refer to

Laser unequal path interferometer configurations by grating splitting at the Fourier plan" , Opt. Eng. 23(5) 646-649, by G. Molesini). This interferometer measures and analyzes a shape of a concave mirror using the diffraction grating as the beam splitter. The interferometer uses diffraction lights of two different orders as the reference light and the light directing to the measurement target object, and one point of the diffraction grating serves as the reference surface. Therefore, unnecessary optical components etc. are not required and hence the interferometer is very simple. However, since the reference surface is one point on the beam splitter, it is not possible to perform phase shifting by a conventional method in which the reference surface is shifted in the direction of an optical axis. If a measurement target object, i.e., a concave spherical mirror is shifted in the direction of the optical axis, a light reflected again at the measurement target object is not focused on one point of the diffraction grating which is the reference point. That is, since the reference surface and the object surface can not directly be moved in the direction of the optical axis, a phase shifter can not be installed.

Disclosure of the Invention

Accordingly, the present invention has been made in view of the above problems, and it is an object of the present invention to provide a phase-shifting interferometer using a diffraction grating which is easily manufactured and can achieve high precision performance as a beam splitter or a light ray path controller, without using a reference mirror.

It is another object of the present invention to provide an interferometer which can construct an optical system so as to apply a phase-shifting algorithm by phase-shifting an object light or a reference light, or both by the control of the shifting of a diffraction grating, and evaluate a measurement object by applying an interference pattern obtained from the optical system to the phase-shifting algorithm. To accomplish the above objects of the present invention, there is provided an interferometer which can simply construct a phase-shifting structure and various types of optical systems, thereby reducing an error of an entire system and the cost of manufacturing and achieving measurement of high precision.

It is to be understood that both the foregoing general description and the following detailed description of the present invention are exemplary and explanatory and are intended to provide further explanation of the invention as claimed.

Brief Description of the Drawings

Further objects and advantages of the invention can be more fully understood from the following detailed description taken in conjunction with the accompanying drawings in which: FIG. 1 illustrates the principle of a phase-shifting diffraction grating interferometer using different diffraction components as a light directing to a measurement target object and a reference light;

FIG. 2A illustrates paths of a light directing to a measurement target object and an object light when lights from a light source are focused on one point of a diffraction grating in the case where the light directing to a measurement target object and the reference light use different diffraction components;

FIG. 2B illustrates a path of a reference light when lights from a light source are focused on one point of a diffraction grating in the case where a light directing to a measurement target object and the reference light use different diffraction components;

FIG. 3 illustrates a phase-shifting diffraction grating interferometer for measuring a concave mirror according to the present invention; FIG. 4 illustrates a phase-shifting diffraction grating interferometer for measuring a plane mirror according to the present invention;

FIG. 5 illustrates a phase-shifting diffraction grating interferometer for measuring a plane mirror by using a diffraction grating of a wide area according to the present invention; FIG. 6 illustrates a phase-shifting diffraction grating interferometer using a transmission type diffraction grating according to the present invention;

FIG. 7A illustrates a transmission type diffraction grating of which grating surface is in the direction of a light source; FIG. 7B illustrates a transmission type diffraction grating of which grating surface is in the opposite direction of a light source;

FIG. 8 illustrates a phase-shifting interferometer in the case where a spherical wave is generated by using an optical fiber according to the present invention; FIG. 9 illustrates a phase-shifting interferometer in the case where lights from a light source are incident upon a diffraction grating at an oblique angle according to the present invention;

FIG. 10 illustrates the principle of a phase-shifting interferometer using a part of one diffraction component as a reference light and using the other part of the one diffraction component as a light directing to a measurement target object, according to the present invention;

FIG. 11A illustrates a path of an object light when lights from a light source are focused on one point of a diffraction grating in the case where a part of one diffraction component is used as a reference light and the other part of the one diffraction component is used as a light directing to a measurement target object, according to the present invention;

FIG. 11B illustrates a path of a reference light when lights from a light sources are focused on one point of a diffraction grating in the case where a part of one diffraction component is used as a reference light and the other part of the one diffraction component is used as a light directing to a measurement target object, according to the present invention;

FIG. 12 illustrates a phase-shifting diffraction grating interferometer for measuring a concave mirror by using a part of a light diffracted with a zero order component at a Littrow mounted diffraction grating as a reference light and using the other part of the light as a light directing to a measurement target object, according to the present invention; and

FIG. 13 is a block diagram of a phase-shifting diffraction interferometer measuring system according to the present invention.

Best Mode for Carrying Out the Invention

The present invention will now be described in detail in connection with preferred embodiments with reference to the accompanying drawings. The present invention relates to an improved diffraction grating interferometer used in the field of an optical metrology. The interferometer includes various types of interferometers which can measure objects of various shapes. The phase-shifting diffraction grating interferometer proposed in the present invention is composed of a light source part, a beam splitter or a light path controller, a phase-shifting controller, an interference pattern generating part, an interference pattern obtaining part, a central processing unit, and a result displaying part. The light source part includes a light source, a lens, a pinhole, and a collimator. These optical elements can be eliminated according to the characteristics of the system or replaced by other optical elements. It is preferable to use a laser with high coherence as the light source used in the light source part in order to easily obtain interference patterns. As the beam splitter or the light path controller, a diffraction grating is used. If necessary, a reflection type diffraction grating or a transmission type diffraction grating is used. The interference pattern generating part generates an interference pattern by causing a reference light to interfere with a light directing to a measurement target object, diffracted again at the diffraction grating after being reflected at the measurement target object. The interference pattern obtaining part obtains the interference patterns generated from the interference pattern generator by an image pickup means, and transmits the acquired interference patterns to the central processing unit. A Charge-Coupled Device (also called

CCD" ) camera is generally used as the image pickup means, but a line type camera may be used if necessary. Other cameras are usable for the image pickup means if they can acquire the interference patterns and digitally process the interference patterns. The phase-shifting controller includes a shifting unit for shifting the diffraction grating in a longitudinal direction, a micro-actuator for micro-actuating the shifting unit, and an actuator driver. A piezoelectric element is widely used as the micro- actuator, but any other actuators designed to be suitable for the system can be used. The central processing unit controls the actuator driver for driving the micro-actuator, and includes algorithms for analyzing the interference patterns obtained from the image pickup means and programs for displaying the analysis results. The central processing unit displays the analysis results through the result displaying part according to the demand of the user.

A few terms used herein will be defined hereinbelow. A light incident upon a diffraction grating from a light source is separated into several diffraction lights. Among these diffraction lights, a light traveling toward an image pickup means is referred to as a " reference light" , and a light traveling toward a measurement target object is referred to as a " light directing to the measurement target object" or a " measurement light" . The light directing to the measurement target object is reflected at the measurement target object, and diffracted into several lights after being incident again upon the diffraction grating. Among the diffracted lights, a light causing interference with the reference light while being toward the image pickup means is referred to as an " object light" . The above terms will easily be appreciated to those skilled in the art. The following description is made based on the above-described terms, but there may be a slight difference in terms according to circumstances or as occasion arises. The principle of using a diffraction grating as a beam splitter will be described in detail hereinafter with reference to FIG. 1. One light incident upon the surface of the diffraction grating is diffracted in a specific direction

according to a wavelength λ and an incident angle 6? . This is represented

by the following diffraction grating equation:

c/(sin r?_m + sin 6',) = A (1)

where d is a diffraction grating groove spacing, m is a diffraction order, and

θ_m is a diffracted angle. The incident angle and the diffracted angle are

measured at a surface perpendicular to the surface of the diffraction grating. The diffracted angle can be expressed by the following Equation (2):

0_ffl = sin-' (ιw- - sin 0₁) (2) d

As can be seen from Equation (2), the diffracted angle is a function of the wavelength of a light source and the diffraction grating groove spacing.

When using the diffraction grating as a beam splitter, a reference light and a light directing to a measurement target object are diffraction lights of different diffraction orders. Assuming that the diffraction order of the reference light is r and the diffraction order of the light directing to the measurement target object is m_{1 (} the diffraction orders of the two lights are not equal: m, ≠ r (3)

Among lights focused on one point, when considering only one incident light 311 perpendicular to a diffraction grating 101, its incident angle is 0°. When using a negative first order diffraction light as a reference light 331 , and a positive first order diffraction light as a light 321 directing to a measurement target object 31 , the two lights have the diffraction orders of - 1 and + 1, respectively, and they are diffracted in the direction of diffraction angles r5>_, and θ_+l obtained by Equation (2).

The negative first order diffraction light 331 travels towards an optical detector, and the positive first order diffraction light 321 is reflected at the measurement target object 31 and diffracted again at the diffraction grating. In this case, the incident angle is θ_+l . Among diffracted lights after being incident upon the diffraction grating at an angle of θ_+l from the measurement target object, a zero order diffraction light travels toward the optical detector with the same diffraction angle as the reference angle. This object light interferes with the reference light.

FIGs. 2A and 2B illustrate an interference phenomenon in the case where an incident light is not perpendicular to a diffraction grating. FIG. 2A illustrates a path of an object light, and FIG. 2B illustrates a path of a reference light. When a light 312 is incident upon one point P of a diffraction grating 102 at an angle of θ_j , a positive first order diffraction light 322 directs to a measurement target object 32 according to the diffraction grating equation. The light 322 is reflected at a point Q on the measurement target object and diffracted at the diffracting grating to take a zero order diffraction light 332 as the object light. A negative first order diffraction light 342 of the light 312 incident upon the diffraction grating at an angle of θ_i directs to the optical detector

as the reference light. However, the light 342 travels at a different angle from the object light 332. The object light causes interference with a reference light 332' which is a positive first order diffraction light of a light 312' incident at an angle of - θ_t with a difference of 180° on the basis of an

optical axis.

In an optical system using a diverging or converging spherical wave, two interference wavefronts have a 180° rotated state with respect to each other. However, if a light source with high spatial coherence is used, no problems arise.

If the above-stated processes are applied throughout the entire areas of the measurement target object as the point Q, interference patterns for a relative distance at the point P for all areas of the measurement target object can be obtained. The interference pattern is represented by the following Equation (4) showing intensity I of any one point. l = A + Bcos(Ω) (4) Equation (4) shows the intensity of one point on the interference pattern and forms the basis of acquiring height information of one point on the measurement target object corresponding to one point on the interference pattern. In Equation (4), A and B are constants, and Ω is a relative phase difference between two lights causing interference. The phase difference can be represented by the following Equation (5):

Ω = 2π^^- + AΩ (5) λ where OPD is a relative light path difference between two interference lights, and ΔΩ is a phase shifted amount which is not caused by the light path difference but caused by shift of the diffraction grating.

When accurately shifting the diffraction grating in the direction of a grating plane, the diffracted light is phase-shifted according to a shifted distance, x. The phase shifted amount of one diffraction light can be represented by the following Equation (6):

AΩ = 2πm- (6) d where m is the diffraction order, and d is the diffraction grating groove grating. There is no phase shifting for m=0, that is, for a zero order diffraction component.

As known by Equation (6), the phase shifted amount is a function of the diffraction order.

The reference light directs to the optical detector as a negative first order diffraction light. Therefore, if the diffraction grating is shifted by x in the direction of the grating plane, the phase shifted amount of the reference light is as follows:

ΔΩ, = ΔΩ_, = -2π- (7) d

The light directing to the measurement target object is diffracted with a positive first order, reflected at the measurement target object, and reflected again at the same point on the diffraction grating with a zero order diffraction component. Therefore, the phase shifted amount of the object light is as follows:

ΔΩ_o = ΔΩ_+l + ΔΩ₀ = +27T- + 0 = +2 r- (8) d d The relative phase shifted amount between the reference light and the object light is the difference between phase shifted amounts of the two lights.

ΔΩ = ΔΩ₀ - ΔΩ,. = +4;r- (9) d

X

Consequently, the relative phase shifting occurs by 4π— between the d reference light and the object light. The light path difference between the two lights is regarded as a constant because it does not vary. Substituting Equation (5) into Equation (4) while substituting Equation (9) into Equation

(5) results in:

OPD x l = A + Bcos(2π^-^- + 4π-) (10) λ d That is, in the case where a negative first order diffraction component is used as the reference light and a positive first order diffraction component is used as the light directing to the measurement target object, if the diffraction grating is accurately shifted by x in the direction of the grating plane without changing the light path difference, the phase shifting arises as shown in Equation (10).

As illustrated in FIG. 1 , the object light has a light path difference by the amount returning from the measurement mirror surface in comparison with the reference light. Assuming that a distance between the point P on the diffraction grating and the point Q on the measurement mirror surface is

R_Q, the light path difference OPD is 2R_Q.

Ω_OPD = 2π ° - = 4π^ (11)

The intensity of the interference pattern corresponding to the point Q is given by the following Equation (12):

I_ρ(k) = A_Q + B_Q cos(4π^ + 4π^-) (12) λ d where AQ and BQ are constants A and B at the point Q, and x(k) is a k-th shifted distance in a longitudinal direction of the diffraction grating. An initial phase value can be obtained by shifting the diffraction grating several times and applying the shifted diffraction grating to a phase-shifting algorithm.

Assuming that the initial phase is Ω_Q , the distance RQ between the points P

and Q can be calculated by:

^{R =}i^ ⁽¹³⁾ If the point Q is defined throughout the entire areas of the measurement target object and the distance RQ between the points P and Q is obtained, it is possible to restore a three-dimensional shape of the measurement target object.

Although it has been assumed in the above description that the negative first order diffraction component is the reference light and the positive first order diffraction component is the light directing to the measurement target object, the interference patterns can be made by using diffraction components of other two orders. It should be noted, however, that phase shifting may not occur when the object light and the reference light have the same phase shifting due to the movement of the diffraction grating.

Assuming that the reference wave directs to the optical detector with an r-th order diffraction component and the diffraction grating is shifted by x in the direction of the grating plane, the phase shifted amount of the reference light obtained by applying Equation (6) is as follows:

ΔΩ_r = 2;zr- (14) d

If the object light directs to the measurement target object with an mi-th order diffraction component and directs to the optical detector with an m₂ ^_th order diffraction component at the same point of the diffraction grating after being reflected at the measurement target object, the phase shifted amount of the object light is as follows:

X X X

AΩ₀ = ΔΩ,„, + ΔΩ_m2 = +2τιm_i — + 2πm₂ — = +2π(m_l + m₂) — (15) d d d The relative phase shifted amount between the reference light and the object light is equal to the difference between phase shifted amounts of the two lights.

ΔΩ = ΔΩ_D - ΔΩ_r = +2Λ-(W, + m₂ - r)— (16) d As can be appreciated from Equation (16), the relative phase difference is a function of diffraction orders of the object light and the reference light. If a value of mι+ m₂-r is 0, the relative phase shifted amount becomes 0. Hence, the following equation (17) should be taken into consideration in designing the interferometer. m_i + m₂ - r ≠ 0 (17)

In other words, the condition of Equation (17) should necessarily be considered in designing the interferometer.

Substituting Equation (5) into Equation (4) while substituting Equation

(16) into Equation (5) results in:

OPD x f = A + Bcos(2π- + 2 r(/n, + m₂ - r)-) (18) λ d

If the distance between the point P on the diffraction grating and any point Q on the measurement mirror surface is RQ, then the light path difference is 2RQ. The intensity of the interference pattern corresponding to the point Q is as follows:

l₀(k) = A₀ + B₀ cos(4π-^- + 2π(m_l + m₂ - r)^-) (19) λ d where AQ and BQ are constants A and B at the point Q, and x(k) is a k-th shifted distance in a longitudinal direction of the diffraction grating. An initial phase value can be obtained by shifting the diffraction grating several times and applying the shifted diffraction grating to a phase-shifting algorithm.

Assuming that the initial phase is Ω_Q , the distance RQ between the points P

and Q can be obtained by Equation (13).

A numerical aperture is mainly used to determine the definition of an objective lens of a microscope and corresponds to a measurement area of a spherical mirror surface in the present invention. If a maximum value of an angle made by an optical axis and a light ray incident upon the objective lens or mirror surface is φ_MAX , and if a diffractive index of a medium between the objective lens and a test material is n (where n=l for air), the numerical aperture is defined by the following Equation (20):

NA = nύnφ_MAX (20)

If the angle between the optical axis of the measurement target object and a point farthest away from the optical axis, directing to the measurement target object is 6>_max , the numerical aperture NAs of the

spherical light incident upon the diffraction grating from the light source should meet the following Equation (21):

N4, > sin(0_max) (21)

The fact that the angle between the spherical mirror to be measured and the axis of the measurement target object is large indicates that a large spherical wave corresponding to that angel is required.

When the wavelength of the light source is fixed, the diffraction grating groove spacing should be sufficiently small so as not overlap the diffraction components. If a light having a large numerical aperture is used, a diffraction grating having a small grating spacing should be selected to avoid overlapping adjacent diffraction components.

If the diffraction grating groove spacing is very small, the diffraction components may not occur. In order to generate the positive first order diffraction component of the spherical wave, a diffraction angle of the positive first order diffraction component of a light incident upon the diffraction grating should be less than 90°.

If a value of the numerical aperture NAs of a light source incident upon the diffraction grating, corresponding to the size of the measurement target object is predetermined, Equation (22) can be obtained according to the diffraction grating equation.

λ ( d (-^— (22)

\ - NA_s 2NA_S

That is, the diffraction grating groove spacing should be determined as a value satisfying Equation (22). Various forms of the diffraction grating interferometers to which the beam splitter of the above-described diffraction grating is applied will now be described.

FIG. 3 illustrates a phase-shifting diffraction grating interferometer for measuring a concave mirror according the present invention. A light starting from a light source 43 passes through a pin hole 63 via a lens 53. A lens 73 causes the light passing through the pin hole 63 to be a parallel light 203. The parallel light 203 concentrates on one point on a reflection type diffraction grating 103 by a lens 83. The light incident upon the diffraction grating is resolved into several lights. One of them is a reference light 233, and another one 223 directs to a measurement target object of the concave mirror. A light reflected at the measurement target object of the concave mirror is incident again upon the diffracting grating and is split into several lights. Among those lights, a diffraction component traveling in the same direction as the reference light is taken as an object light. The object light generates an interference pattern by interference with the reference light. A light passing through a lens 1 13 and an iris 123 passes through a lens 133 and forms an image to be provided to an image pickup means 23. A CCD camera is generally used as the image pickup means but any device may be used if it can convert the image into an electric signal. A central processing unit 13 processes and restores the image, and controls a phase-shifting driver to generate phase shifting. Moreover, the central processing unit 13 commands the phase-shifting driver to apply a signal to a phase-shifting controller 153. As a function of processing the image, the central processing unit 13 directly displays the image or interference pattern acquired by the image pickup means 23, or graphically displays height information of the measurement target object obtained by analyzing the interference patterns. Further, the central processing unit 13 displays data and three-dimensional shape information, obtained through the height information. The phase-shifting controller includes a shifting unit using a piezoelectric element. The shifting unit adjusts directions and angles so as to continuously focus the light 213 and the reflected light 223 on one point of the diffraction grating, and shifts the diffraction grating in the longitudinal direction.

FIG. 4 illustrates a phase-shifting diffraction grating interferometer for measuring a plane mirror according to the present invention. A spherical light 224 directing to a measurement target object 34 is changed to a parallel light 244 by a light path change means 164. The parallel light incident vertically upon the measurement object 34 is reflected and concentrates on one point of a diffraction grating 104, thereby causing interference with a reference light 234. A central processing unit 13 and a phase-shifting controller 154 perform the same function as those in FIG. 3.

As noted above, various kinds of measurement target objects, for example, non-spherical surfaces can be measured by introducing the light path change means 164 between the measurement target object 34 and the diffraction grating 104. As the light path change means, a null lens or a CGH (Computer Generated Hologram) is used according to the shape of the measurement target object.

If the reflectivity of the measurement target object is low, or the efficiency of the CGH is low, the intensity of the measurement light is low and the visibility may be deteriorated. In this case, the intensity of the measurement light can be raised in comparison with the reference light by using a blazed grating. The blazed grating is designed in such a manner that the intensity of a specific diffraction component is higher than that of other diffraction components. Therefore, it is possible to arrange the intensity of the light directing to the measurement target object is higher than that of the reference light in order to relatively compensate for the intensity of the light directing to the measurement target object.

FIG. 5 illustrates another example of a phase-shifting interferometer for measuring a plane mirror. This interferometer uses not a part of a diffraction grating but the diffraction grating of an area similar to a measurement target object. A light starting from a light source 45 converges by a lens 55, and passes through an aperture 65. The light passing through the aperture 65 becomes a parallel light 215 of a large area by a lens 75 and is diffracted by a diffraction grating 105 of a large area. If a collimated light is incident upon the diffraction grating, there is no rotation of a wavefront. When shifting the diffraction grating, however, the same phase shifting arises for all lights. The interference light passing through a lens 115 and an iris 125 passes through a lens 135 and is obtained as an image by an image pickup means 25. FIG. 6 illustrates a phase-shifting diffraction grating interferometer using a transmission type diffraction grating as a beam splitter. The diffraction grating has a grating surface at its back. A light starting from a light source passes through a lens 86 and concentrates on one point of a transmission type diffraction grating 106. Like the interferometer stated above, one diffraction light 226 is set as a light directing to a measurement target object, and another light 236 is set as a reference light. A process of forming and acquiring an interference pattern is identical to that described above. FIGs 7A and 7B illustrate transmission type diffraction gratings In FIG 7A, a grating surface is in the direction of a light source, and in FIG 7B, a grating surface is in the opposite direction of the light source A glass plate with a transmission type diffraction grating generates an aberration due to its thickness and diffractive index. In FIG 7A, after a light is split at the diffraction grating, a measurement light passes through a glass surface three times and a reference light passes through the glass surface one time Consequently, the measurement light is influenced by the aberration twice as often as the reference light by two times In FIG 7B, since a light is split after passing through the glass surface with a diffraction grating groove, the measurement object and the reference light have the same aberration and the interference pattern is not affected by the aberration

When the transmission type diffraction grating is used, it may be difficult to perform measurement due to various aberration components In this case, the aberration components can be eliminated by using auxiliary optical elements, or a system error can be removed only by software These aberration components do not appear in the interferometer using the reflection type diffraction grating

Even when using the transmission type diffraction grating, a plane of a large area can be measured by adding the light path change part 164 as shown in FIG 4 If lights concentrate on one point of the diffraction grating, the two interference wavefronts are in a rotated state by 180° with respect to each other as described in conjunction with FIG 2 However, if a light source with high coherence is used, no problems arise As another form for measuring a plane, the transmission type diffraction grating of a large area is used as illustrated in FIG. 5. In this case, there is no rotation of the wavefronts.

FIG. 8 illustrates a phase-shifting diffraction grating interferometer using an optical fiber. Instead of a lens with high performance, the principle of an optical fiber is utilized to generate a spherical wave. That is, if a light is incident upon a single mode optical fiber, the spherical wave is generated from an end of the optical fiber. A light starting from a light source 48 arrives at a single mode optical fiber 188 through a lens 58. An end of the optical fiber is perpendicularly installed to the grating surface of a diffraction grating 108 so as to nearly touch one point of the diffraction grating. The spherical wave generated from the end of the optical fiber is separated into diffraction components of several orders from the diffraction grating. One diffraction light 228 is set as a light directing to a measurement target object, and another light 238 is set as a reference light. Among diffraction components incident again upon the diffraction grating after being reflected at the measurement target object, a light diffracted in the same direction as the reference light is set as an object light and causes interference with the reference light. If a shifting unit 158 is shifted toward the diffraction grating, two interference lights are phase-shifted. In this case, the end of the optical fiber is installed so as not to touch the diffraction grating, thereby preventing the surface of the diffraction grating from being damaged by the end of the optical fiber when the diffraction grating is shifted. If the optical fiber is replaced by the lens, the optical system has the same configuration as that shown in FIG. 7A. Hence, the aberration component should be eliminated when using the transmission type diffraction grating, and there is no aberration component when using the reflection type diffraction grating.

While the above embodiments have shown the light incident vertically upon the diffraction grating from the light source, FIG. 9 illustrates a phase- shifting interferometer in the case where a light is incident upon the diffraction grating at an oblique angle. A positive first order diffraction component of a light starting from a light source 49 is aligned with a vertical surface of a diffraction grating 109. A light starting from the light source 49 passes through an aperture 69 via a lens 59 and becomes a parallel light by a lens 79. The parallel light concentrates on one point of the diffraction grating 109 by a lens 89. A zero order diffraction component serving as a reference light is reflected at the diffraction grating 109 and travels toward a lens. 119. A negative first order diffraction component 229 directs to a mirror surface 39. A light reflected at the mirror surface 39 is incident vertically upon the diffraction grating and is separated into several diffraction components. Among these diffraction components, a negative first order diffraction component diffracted in the same direction as the reference light becomes an object light. The object light interferes with the reference light and generates an interference pattern. In this case, since the shape of a measurement target object is formed in an optical detector through the diffraction grating, if the mirror surface has a circular form, the interference pattern is an elliptical shape. In order to restore the circular form, the circular information of- the mirror surface should be restored by software.

If the diffraction grating is sifted in the direction of the grating plane, the diffraction light is phase-shifted according to a shifted distance x. The phase shifted amount can easily be known by applying the above-proposed phase-shifting equation. Since the reference light has a zero order component, r is 0. Since the object light is diffracted twice with a negative first order component, mi and π ₂ are - 1. The relative phase shifted amount between the reference light and the object light is as follows:

AΩ = AΩ_o - AΩ_r = 2π(m_i + m₂ - r)- = -4π- (23) d d x Consequently, the relative phase shifting occurs by 4π— between the d reference light and the object light. The light path difference between the two lights is regarded as a constant because it does not vary. Let the optical path difference be OPD. If Equation (4) is applied, then:

ΩPD x

I = l₀ + VI₀ cos(2π^-^ - 4π-) (24) λ d

That is, even if the light is incident upon the diffraction grating at an oblique angle, the reference light and the object light are selected to acquire the interference pattern. If the diffraction grating is accurately shifted in the direction of the grating plane by x without modifying the light path difference, the phase can be shifted as represented by Equation (24). It is also possible to design interferometers of other forms by properly selecting diffraction order values mi, m₂ and r satisfying Equation (20).

FIG. 10 illustrates the principle of an interferometer using a diffraction grating as not a beam splitter but simply a light path controller by employing one diffraction light among diffraction lights. A diffraction grating 500 is arranged in such a manner that when a light is incident upon the diffraction grating in the direction of an optical axis from a measurement target object and an optical detector, a reflective light diffracted with a positive first order at the diffraction grating can travel in an incident direction. The case where the diffraction light of a light incident upon the diffraction grating travels towards the incident direction is referred to as " Littrow mount" .

Assuming that an angle incident upon the diffraction grating is θ_d , an angle

diffracted with a positive first order at the diffraction grating is also θ_tl .

From Equation (1), the following Equation (25) is obtained for the same

incident angle and diffracted angle of θ_(l .

d(sm θ_d + &m θ_ll) = λ (25) λ where θ_ll = sm^~l ( — ) . 2d

If the light is incident upon the diffraction grating in the direction of the optical axis, the positive first order diffraction light travels in the same direction. If a light traveling upward from the optical axis is incident again upon the diffraction grating, the positive first order diffraction light travels downward due to the inverted wavefront. In this case, the diffraction order of the reference light is equal to that of the light directing to the measurement target object. m_t = r (26)

To aid understanding, it is assumed that a part of the zero order reflective diffraction component among incident lights is selected as the reference light and the other part is selected as the light directing to the measurement target object. A spherical light 601 starting from a light source with high coherence is incident upon a diffraction grating 500 at an incident angle - θ_d . The spherical light is reflected and diffracted with a zero order

at one point P on the diffraction grating, and travels toward a mirror surface

430 and an optical detector at a zero order diffraction angle θ_d at a position

perpendicular to the diffraction grating. A light 630 positioned in a downward direction of the optical axis travels to the optical detector as the reference light. A light 620 positioned in an upward direction of the optical axis is reflected at the mirror surface and converges on one point P of the diffraction grating as a light directing to the measurement target object. A component diffracted with the positive first order at the point P of the diffraction grating is taken as the object light. The object light traveling toward the optical detector causes interference with the reference light. An interference phenomenon of one light traveling to one point Q of a measurement target object, among lights incident upon one point of a diffraction grating will now be described with reference to FIGs. 11A and 11B. FIG. 11A illustrates a path of an object light. A light 611 starting from a light source is incident at an angle of - θ_d with an optical axis and at an

angle oϊ- θ - θ_d with a line perpendicular to the diffraction grating. Since the

light 61 1 is diffracted with a zero order at the diffraction grating, it directs to one point Q of the measurement target object. A light 621 reflected at the measurement target object is incident again upon one point P of the diffraction grating. A light 631 diffracted with the positive first order at the point P of the diffraction grating travels to an optical detector as the object light. The direction of the object light directing to the optical detector can be obtained by applying the diffraction grating equation. Θ_D θ_d - sm ^l(2s θ_d - sm(θ_d + θ)) (27)

This object light causes interference with a light 611' incident at an angle Θ_D with an optical axis, as illustrated in FIG. 11B. When applying the same process by setting a point Q throughout the entire areas, the interference patterns for a relative distance between a point P and the entire areas of the measurement target object can be obtained.

The interference pattern is represented by the following equation (28) showing the intensity I of any one point. l = A + Bcos(Ω) (28)

Equation (28) shows the intensity of one point on the interference pattern and forms the basis of acquiring height information of one point of the measurement target object. In Equation (28), A and B are constants, and

Ω is a relative phase difference between two lights causing interference.

The phase difference is given by the following Equation (29): Ω = 2π^-^ + AΩ (29) λ

If the diffraction grating is accurately shifted in the direction of a grating plane, the diffracted light is phase-shifted according to a shifted distance, x. The phase shifted amount can easily be known by applying the above-proposed phase shifting equation. Since the reference light is a zero order component, r is 0. Since the object light is diffracted with the zero order component and then diffracted with a positive first order component, mi and ni2 are 0 and + 1, respectively.

From Equation (16), the relative phase shifted amount between the reference light and the object light is given by the following Equation (30):

ΔΩ = ΔΩ - ΔΩ = 2π(m. + m, - r)- = 2π- (30)

^{1 2} d d

X

That is, the phase is shifted by 2π— between the reference light and d the object light. The light path difference between the two lights is regarded as a constant because it does not vary. Let the optical path difference be OPD. If Equation (29) is substituted into Equation (28) while Equation (30) being substituted into Equation (29), then:

I = A + B cos(2π^^- + 2π-) (31) λ d

In an interferometer using only one diffraction component as the reference light and the light directing to the measurement target object among Littrow mounted lights incident upon the diffraction grating, if the diffraction grating is accurately shifted by x in the direction of the grating plane without modifying the light path difference, phase shifting can arise as indicated in the above equation. It is possible to design interferometers using other diffracted lights as the reference light and the light directing to the measurement target object by properly arranging the diffraction grating.

Since half of one light directs to the measurement target object, if the angle between a point farthest away from the optical axis of the measurement target object and the optical axis is θ_mm , an angle formed by the light incident upon the diffraction grating and the point farthest away from the optical axis of the measurement target object is 2θ_max .

The numerical aperture NAs of the spherical light incident upon the diffraction grating from the light source should meet the following Equation (32):

NA_S ) sϊn(2θ_mΛX) (32)

In order to prevent unnecessary diffraction components from being overlapped, the diffraction grating groove spacing should satisfy the following condition:

NA_s ( tan(θ_d) (33)

A description will now be made of an interferometer merely using a diffraction grating as a light path controller by employing one diffraction component as a reference light and a light directing to a measurement target object.

FIG. 12 illustrates a phase-shifting diffraction grating interferometer for measuring a concave mirror according to the present invention. A light starting from a light source 442 becomes a parallel light 602 via a lens 452, a pin hole 462, and a lens 472. A lens 482 causes the parallel light 602 to concentrate on one point on a reflection type diffraction grating 502. A zero order diffraction component of the light incident upon the diffraction grating directs to a measurement target object 432 and an optical detector 422. A light 632 positioned in a downward direction of the optical axis is selected as the reference light, and a light 622 positioned in an upward direction of the optical axis is selected as a light directing to the measurement target object. A light reflected at the measurement target object is focused again on one point of the diffraction grating and diffracted with a positive first order component at the diffraction grating. The positive first order reflected diffraction component has the same direction as the reference light and is taken as the object light. The object light causes interference with the reference light and generates an interference pattern. The object light and the reference light pass through a lens 512 and an iris 522 and form an image, by a lens 532, to be provided to an image pickup means 422. A shifting unit 552 shifts the diffraction grating in a longitudinal direction so that the incident light from the light source can continuously be focused on one point of the diffraction grating. A central processing unit and a phase- shifting controller have the same functions as those in FIG. 3.

Like examples using the diffraction grating as the beam splitter, even the phase-shifting diffraction grating interferometer using one diffraction component as the reference light and the light directing to the measurement target object can measure various types of measurement objects, use a transmission type diffraction grating, and replace a light source part by an optical fiber.

A measuring process for the diffraction grating phase-shifting interferometer based on the above-stated equations includes a first step of irradiating a light source to a diffraction grating; a second step of selecting a light diffracted with an mi-th order component at the diffraction grating as a light directing to a measurement target object; a third step of selecting a light diffracted with an r-th order component at the diffraction grating as a reference light; a fourth step of irradiating, to the diffraction grating, a light reflected by irradiating, to the measurement target object, the light directing to the measurement target object; a fifth step of selecting, as an object light, a light diffracted with an m₂ ^_th order component in the same direction as the reference light, among diffraction lights incident upon the diffraction grating, and generating an interference pattern by causing the object light to interfere with the reference light; a sixth step of acquiring the generated interference pattern with an image pickup means; a seventh step of generating another interference pattern by shifting the diffraction grating by a micro-distance; an eighth step of repeating the sixth and seventh steps to obtain a plurality of interference patterns; and a ninth step of measuring a three — dimensional shape of the measurement target object through an analysis algorithm for the obtained interference patterns.

FIG. 13 illustrates a configuration of a phase-shifting diffraction grating interferometer. The interferometer is composed of a central processing unit 710, a light source 721, a phase-shifting controller 720, an interference pattern generating part 730, and an interference pattern obtaining part 740. The central processing unit 710 includes a phase- shifting driver 712, an operator 713 for analyzing an interference pattern, an image processing/displaying part 714 for processing and displaying operation results, and a controller 711. The phase-shifting controller 720 includes a shifting unit/micro-actuator 723 for shifting a diffraction grating 722. The interference pattern generating part 730 generates an interference pattern by combining a measurement light 731 with a reference light 732. The interference pattern obtaining part 740 includes an image pickup means 741 and an image pickup means controller 742. The above interferometer shows a basic configuration, and other elements may be added or eliminated according to the characteristics of the interferometer.

While the present invention has been described with reference to the particular illustrative embodiments, it is not to be restricted by the embodiments but only by the appended claimed. It is to be appreciated that those skilled in the art can change or modify the embodiments without departing from the scope and spirit of the present invention.

Claims

What is claimed is:

1. A phase-shifting diffraction grating interferometer, comprising: a light source part for supplying a light; a diffraction grating for separating the light into several diffraction components; a light directing to a measurement target object, diffracted with a prescribed order (mi) component among the diffraction components; a reference light traveling toward an optical detector, diffracted with another prescribed order (r) component among the diffraction components; an object light diffracted with a specific order (111₂) component in the same direction as the reference light, among lights diffracted after the light directing to the measurement target object is reflected at the measurement target object and is incident again upon the diffraction grating, thereby generating an interference pattern together with the reference light; an interference pattern obtaining part for obtaining the interference pattern; a phase-shifting controller for generating phase shifting by shifting the diffraction grating in a longitudinal direction; a central processing unit for analyzing interference pattern information obtained from the interference pattern obtaining part through a measurement algorithm; and a displaying part for displaying the analyzed results.

2. The phase-shifting diffraction grating interferometer of claim 1 , wherein diffraction lights having different diffraction orders are selected as the reference light and the light directing to the measurement target object, by satisfying a condition that the diffraction order mi of the light directing to the measurement target object is not equal to the diffraction order r of the reference light (ml ≠ r)

3. The phase-shifting diffraction grating interferometer of claim 1 , wherein the diffraction grating is of a reflection type.

4. The phase-shifting diffraction grating interferometer of claim 1 , wherein the diffraction grating is of a transmission type.

5. The phase-shifting diffraction grating interferometer of any one of claims 1 to 4, wherein the diffraction grating creates a diffraction phenomenon on a diffraction grating surface positioned in the same direction as the light source part.

6. The phase-shifting diffraction grating interferometer of any one of claims 1 to 4, wherein the diffraction grating creates a diffraction phenomenon on a diffraction grating surface positioned in the opposite direction to the light source part.

7. The phase-shifting diffraction grating interferometer of claim 1 , wherein a light incident upon the diffraction grating from the light source part arrives by an optical system composed of a pin hole and a lens which is a light path change part.

8. The phase-shifting diffraction grating interferometer of claim 7, wherein the light incident upon the diffraction grating is a parallel light.

9. The phase-shifting diffraction grating interferometer of claim 7, wherein the light incident upon the diffraction grating is a convergent light.

10. The phase-shifting diffraction grating interferometer of claim 1 , wherein a light incident upon the diffraction grating from the light source part arrives through an optical fiber.

11. The phase-shifting diffraction grating interferometer of claim 1 , wherein the phase-shifting controller comprises a shifting unit for shifting the diffraction grating in a longitudinal direction, a micro-actuator for micro-actuating the shifting unit, and an actuator driver for driving the micro-actuator.

12. The phase-shifting diffraction grating interferometer of claim 11 , wherein the micro-actuator is driven by using a piezoelectric element.

13. The phase-shifting diffraction grating interferometer of claim 1 , wherein a light path change part is positioned between the diffraction grating and the measurement target object to change a light path according to the shape of the measurement target object.

14. The phase-shifting diffraction grating interferometer of claim 1 , wherein the measurement algorithm selects a light diffracted with the mι~th order component at the diffraction grating as the light directing to the measurement target object, uses a light diffracted with the r-th order component traveling to the optical detector as the reference light, selects, as the object light, a light diffracted with the m₂ ^_th order component among lights diffracted after being reflected at the measurement target object and being incident again upon the diffraction grating thus to generate the interference pattern, calculates a phase shifted amount of the reference light and the light directing to the measurement target light according to a shifted distance of the diffraction grating, calculates a relative phase shifted amount from the phase shifted amount of the light directing to the measurement target object and the phase shifted amount of the reference light, and measures a three-dimensional shape of the measurement target object by applying the relative phase shifted amount to a known phase-shifting algorithm.

15. The phase-shifting diffraction grating interferometer of claim 1 or 14, wherein the relationship among the diffraction order mi of the light directing to the measurement target object, the diffraction order r of the reference light, and the diffraction order m₂ of the object light satisfies a condition of , + m₂ - r ≠ 0 .

16. A phase-shifting diffraction grating interferometer, comprising: a light source incident upon a diffraction grating: a light directing to a measurement target object, diffracted with a prescribed order (mi) component; a reference light traveling toward an optical detector, diffracted with another prescribed order (r) component; an object light diffracted with a specific order (111₂) component in the same direction as the reference light, among lights diffracted after being reflected at the measurement target object and being incident again upon the diffraction grating, thus to generate an interference pattern; wherein the intensity I for one point of the interference pattern obtained by interference of the object light and the reference light is given by the following Equation (a):

OPD x I = A + Bcos(2π + 2π(m_t + m₂ - r)—) (a) λ d

(where A and B are constants, OPD is a relative light path difference between the object light and the reference light, d is a diffraction grating groove spacing, and x is a shifted distance in a longitudinal distance of the diffraction grating), and if 2R_Q is substituted into OPD of Equation (a), then the intensity I<a(k) obtained by k-th shifting the diffraction grating in a longitudinal direction, is represented by the following Equation (b):

I₀(k) = A₀ + B₀ cos(4π— + 2π(m_l + m₂ - r)^-) (b)

A d

(where k=l ,--- ,n, AQ and BQ are constants A and B at the point Q on the measurement target object, x(k) is a k-th shifted distance in a longitudinal direction of the diffraction grating, RQ is a distance between one point of the diffraction grating and one point of the measurement target object, and the relative light path difference OPD is 2RQ), an initial phase value is obtained through the intensity Iq(k) by applying a phase-shifting algorithm, RQ is obtained from the initial phase value, a distance between all points of the measurement target object and one point of the diffraction grating is calculated, and a three-dimensional shape is restored.

17. The phase-shifting diffraction grating interferometer of any one of claims 1 , 14 and 16, wherein a part of one diffraction light is selected as the reference light and the other part of the one diffraction light is selected as the light directing to the measurement target object, thereby satisfying a condition that the diffraction order mi of the light directing to the measurement target object is equal to the diffraction order r of the reference light (ml=r).

18. A measurement method for a phase-shifting diffraction grating interferometer, comprising the steps of: (a) irradiating a light source to a diffraction grating;

(b) selecting a light diffracted with a prescribed order component at the diffraction grating as a light directing to a measurement target object;

(c) selecting a light diffracted with another prescribed order component at the diffraction grating as a reference light;

(d) irradiating, to the diffraction grating, a light reflected by irradiating, to the measurement target object, the light directing to the measurement target object;

(e) selecting, as an object light, a light diffracted with a specific order component in the same direction as the reference light, among diffraction lights incident upon the diffraction grating, and generating an interference pattern by causing the object light to interfere with the reference light;

(f) acquiring the generated interference pattern with an image pickup means; (g) generating another interference pattern by shifting the diffraction grating by a micro-distance;

(h) repeatedly performing the steps (f) and (g) to obtain a plurality of interference patterns; and

(i) measuring a three — dimensional shape of the measurement target object through an analysis algorithm for the obtained interference patterns.