System and method for 3D shape measurement of freeform surface based on high-speed deflectometry using composite patterns

Abstract

The present disclosure is related to a system and a method for 3D shape measurement of a freeform surface based on high-speed deflectometry using composite patterns. More particularly, a system for profile measurement based on high-speed deflectometry using composite patterns includes: a composite pattern generation part to project a composite pattern generated by synthesizing patterns having different frequencies to a measurement object; a detector to acquire images of a deformed composite pattern reflected from the measurement object; and a phase acquisition part to acquire wrapped phases by each frequency from the composite pattern and unwrapped phases from the respective wrapped phases.

Claims

1. A system for profile measurement based on high-speed deflectometry using composite patterns, the system comprising: a composite pattern generation part configured to project, to a measurement object, a plurality of composite patterns having different frequencies for composite patterns generated by synthesizing a pattern in a first direction and a pattern in a second direction; a detector configured to acquire images of a plurality of deformed composite patterns reflected from the measurement object; and a phase acquisition part comprising: an independent pattern extraction part and a regularization part; a wrapped phase extraction part configured to extract wrapped phases for each of a plurality of patterns of the independent extraction part in the first direction from a plurality of spatial phase-shifting patterns moved in a pixel unit from regularized sine patterns of the regularization part, and wrapped phases for each of the plurality of patterns in the second direction; an unwrapped phase acquisition part configured to acquire unwrapped phases for the patterns in the first direction based on a phase difference of the plurality of wrapped phases for the patterns in the first direction, and further configured to acquire unwrapped phases for the patterns in the second direction based on a phase difference of the plurality of the wrapped phases for the patterns in the second direction; and an analyzing means configured to measure and analyze a 3D shape of the measurement object from the acquired unwrapped phases.

2. The system for profile measurement based on high-speed deflectometry using composite patterns according to claim 1, wherein a composite pattern is generated by synthesizing a pattern in the first direction, a pattern in the second direction, a pattern in a third direction rotated 45 degrees in a clockwise direction from the pattern in the second direction, and a pattern in a fourth direction rotated 45 degrees in a counterclockwise direction from the pattern in the second direction.

3. The system for profile measurement based on high-speed deflectometry using composite patterns according to claim 2, wherein the independent pattern extraction part is configured to decompose, through Fourier transform, each of the acquired images of the composite patterns into the respective independent patterns in the first direction and the second direction.

4. The system for profile measurement based on high-speed deflectometry using composite patterns according to claim 3, wherein the regularization part is configured to regularize the sine patterns for each of the independent patterns extracted by the independent pattern extraction part.

5. The system for profile measurement based on high-speed deflectometry using composite patterns according to claim 4, wherein the regularization part applies Lissajous figure and Ellipse fitting method to nonregularized sine pattern signals, so as to regularize the sine patterns.

6. The system for profile measurement based on high-speed deflectometry using composite patterns according to claim 5, wherein the wrapped phase extraction part is configured to obtain the plurality of spatial phase-shifting patterns moved in the pixel unit from the regularized sine patterns for each pattern in the first direction and the second direction, then configured to acquire phase shifts for each of the spatial phase shifting patterns, wherein the wrapped phases are thus extracted for each pattern in the first direction and the second direction therefrom.

7. The system for profile measurement based on high-speed deflectometry using composite patterns according to claim 6, wherein the unwrapped phase acquisition part is configured to acquire unwrapped phases for patterns in the first direction and the second direction by obtaining one cycle of phases for the patterns in the first direction and the second direction.

8. A method of profile measurement based on high-speed deflectometry using composite patterns, the method comprising: projecting, by a composite generation part, to a measurement object, a plurality of composite patterns having different frequencies for the composite patterns generated by synthesizing a pattern in a first direction and a pattern in a second direction; acquiring, by a detector, a plurality of deformed composite patterns reflected from the measurement object; providing an independent extraction part and a regularization part; extracting, by a wrapped phase extraction part, wrapped phases for each of a plurality of patterns of the independent extraction part in the first direction from a plurality of spatial phase-shifting patterns moved in a pixel unit from regularized sine patterns of the regularization part, and wrapped phases for each of the plurality of patterns in the second direction; acquiring, by an unwrapped phase acquisition part, unwrapped phases for the patterns in the first direction based on a phase difference of the plurality of wrapped phases for the patterns in the first direction, and further configured to acquire unwrapped phases for the patterns in the second direction based on a phase difference of the plurality of the wrapped phases for the patterns in the second direction; and measuring and analyzing, by an analyzing means, a 3D shape of the measurement object from the acquired phases.

9. The method of profile measurement based on high-speed deflectometry using composite patterns according to claim 8, wherein the method comprises: decomposing, by the independent pattern extraction part, through Fourier transform, each of the acquired images of the composite patterns into the respective independent patterns in the first direction to the fourth direction; and regularizing, by the regularization part, the sine patterns for each of the independent patterns extracted by the independent pattern extraction part.

10. The method of profile measurement based on high-speed deflectometry using composite patterns according to claim 9, wherein regularizing applies Lissajous figure and Ellipse fitting method to nonregularized sine pattern signals, so as to regularize sine patterns.

11. A system for profile measurement based on high-speed deflectometry using composite patterns, the system comprising: a composite pattern generation part configured to project, to a measurement object, a plurality of composite patterns having different frequencies for composite patterns generated by synthesizing a pattern in a first direction and a pattern in a second direction; a detector configured to acquire images of a plurality of deformed composite patterns reflected from the measurement object; a phase acquisition part comprising: an independent pattern extraction part configured to decompose, through Fourier transform, each of the acquired images of the plurality of composite patterns into each independent pattern of the plurality of patterns in the first direction and the second direction; a regularization part configured to regularize sine patterns for the plurality of the patterns in the first direction and the second direction extracted by the independent pattern extraction part; a wrapped phase extraction part configured to extract wrapped phases for each of the plurality of patterns in the first direction from a plurality of spatial phase-shifting patterns moved in a pixel unit from the regularized sine patterns and wrapped phases for each of the plurality of patterns in the second direction; and an unwrapped phase acquisition part configured to acquire unwrapped phases for the patterns in the first direction based on a phase difference of the plurality of wrapped phases for the patterns in the first direction, and configured to acquire unwrapped phases for the patterns in the second direction based on a phase difference of the plurality of wrapped phases for the patterns in the second direction; and an analyzing means configured to measure and analyze, a 3D shape of the measurement object from the acquired phases.

12. A method of profile measurement based on high-speed deflectometry using composite patterns, the method comprising: projecting, by a composite pattern generation part, to a measurement object, a plurality of composite patterns having different frequencies for composite patterns generated by synthesizing a pattern in a first direction and a pattern in a second direction; acquiring, by a detector, images of a plurality of deformed composite patterns reflected from the measurement object; decomposing, by an independent pattern extraction part, through Fourier transform method, each of the acquired images of the plurality of composite patterns into each independent pattern of the plurality of patterns in the first direction and the second direction; regularizing, by a regularization part, sine patterns for the plurality of the patterns in the first direction and the second direction extracted by the independent pattern extraction part; extracting, by a wrapped phase extraction part, wrapped phases for each of the plurality of patterns in the first direction from a plurality of spatial phase-shifting patterns moved in a pixel unit from the regularized sine patterns and wrapped phases for each of the plurality of patterns in the second direction; acquiring, by an unwrapped phase acquisition part, unwrapped phases for the patterns in the first direction based on a phase difference of the plurality of wrapped phases for the patterns in the first direction, and acquiring unwrapped phases for the patterns in the second direction based on a phase difference of the plurality of the wrapped phases for the patterns in the second direction; and measuring and analyzing, by an analyzing means, a 3D shape of the measurement object from the acquired phases.

13. The system for profile measurement based on high-speed deflectometry using composite patterns according to claim 1, wherein the first direction is a vertical direction and the second direction is a horizontal direction.

14. The method of profile measurement based on high-speed deflectometry using composite patterns according to claim 8, wherein the first direction is a vertical direction and the second direction is a horizontal direction.

15. The system for profile measurement based on high-speed deflectometry using composite patterns according to claim 11, wherein the first direction is a vertical direction and the second direction is a horizontal direction.

16. The method of profile measurement based on high-speed deflectometry using composite patterns according to claim 12, wherein the first direction is a vertical direction and the second direction is a horizontal direction.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The accompanying drawings of this specification exemplify a preferred embodiment of the present disclosure, the spirit of the present disclosure will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings, and thus it will be understood that the present disclosure is not limited to only contents illustrated in the accompanying drawings.

(2) FIG. 1 is a schematic view of a system for 3D shape measurement based on deflectometry.

(3) FIG. 2 is a view of the construction of a system for profile measurement based on high-speed deflectometry using composite patterns in accordance with the present disclosure.

(4) FIG. 3 is a flowchart of a method for profile measurement based on high-speed deflectometry using composite patterns in accordance with the first embodiment of the present disclosure.

(5) FIG. 4 is a view showing a method for generating a composite pattern by synthesizing 4 or more different patterns, by a composite pattern generation part in accordance with the first embodiment of the present disclosure.

(6) FIG. 5 is a view showing a method for extracting 4 independent phases from a composite pattern through Fourier transform by an independent pattern extraction part in accordance with the first embodiment of the present disclosure.

(7) FIG. 6 is a view showing frequency component analysis of a composite pattern and positions of each filter in the Fourier area in association with the first embodiment of the present disclosure.

(8) FIG. 7 shows each shape of filters in the Fourier area for decomposing a composite pattern into 4 patterns in association with the first embodiment of the present disclosure.

(9) FIG. 8 is a view showing a method for generating Lissajous figure and regularizing patterns for applying spatial-carrier frequency phase-shifting method (SCFPS) in association with the first embodiment of the present disclosure.

(10) FIG. 9 is a flowchart of a method for shape measurement based on high-speed deflectometry using composite patterns in association with the second embodiment of the present disclosure.

(11) FIG. 10 is a flowchart for acquiring unwrapped phases using spatial-carrier frequency phase-shifting method (SCFPS) in 3 composite patterns having different frequencies in association with the second embodiment of the present disclosure.

(12) FIG. 11 shows a method for extracting independent patterns in the first and second directions from a composite pattern through Fourier transform, by an independent pattern extraction part in association with the second embodiment of the present disclosure.

REFERENCE NUMBERS

(13) 1: Measurement object 10: Composite pattern generation part 20: Detector 30: Phase acquisition part 31: Independent pattern extraction part 32: Regularization part 33: Wrapped phase extraction part 34: Unwrapped phase acquisition part 40: Analyzing means 100: System for profile measurement based on high-speed deflectometry using composite patterns

DETAILED DESCRIPTION

Best Mode

(14) Hereinafter, described are, in association with an embodiment of the present disclosure, the construction, functions of a system 100 for profile measurement based on high speed deflectometry using composite patterns and a method for profile measurement. FIG. 1 is a schematic view of a system 100 for 3D shape measurement based on deflectometry. And, FIG. 2 is a view of the construction of a system 100 for profile measurement based on high-speed deflectometry using composite patterns in accordance with the present disclosure.

(15) In association with an embodiment of the present disclosure, provided are a system 100 and a method for 3D shape measurement of a measurement object at high speed in deflectometry.

(16) The system 100 for profile measurement based on high speed deflectometry using composite patterns according to an embodiment of the present disclosure may be constructed to include a composite pattern generation part 10 which generates and projects a composite pattern to a measurement object, a detector 20 which acquires an image of a deformed composite pattern reflected from the measurement object 1, a phase acquisition part 30 which acquires each wrapped phase by each frequency from the composite pattern, and acquires each unwrapped phases from the wrapped phases, and an analyzing means 40 which measures and analyzes 3D shape of the measurement object from the acquired phases.

(17) FIG. 1 is a schematic view of a system 100 for 3D shape measurement based on deflectometry. The composite pattern generation part 10 in association with the present disclosure projects, to the measurement object, the composite pattern generated by synthesizing patterns having different frequencies. And the detector 20 acquires an image of a deformed composite pattern reflected from the measurement object. Further, the phase acquisition part 30 acquires each wrapped phase by each frequency from the composite pattern, and acquires each unwrapped phases from the wrapped phases. Further, the analyzing means 40 analyzes the deformed phases measured in the detector 20, so as to obtain the 3D shape of the measurement object 1. Further, a control part is connected to both the composite pattern generation part 10 and the detector 20, thus controlling the both of them. As described in detail hereinafter, the phase acquisition part 30 in association with an embodiment of the present disclosure may be constructed to include an independent pattern extraction part 31, a regularization part 32, a wrapped phase measurement part and an unwrapped phase acquisition part 34.

DESCRIPTION OF EMBODIMENTS

(18) Hereinafter, described in more detail is a method for profile measurement based on high-speed deflectometry using composite patterns in association with a first embodiment of the present disclosure. Firstly, FIG. 3 is a flow chart of the method for profile measurement based on high-speed deflectometry using composite patterns in accordance with the first embodiment of the present disclosure.

(19) The first embodiment of the present disclosure is related to unwrapping algorithm using a composite pattern having 4 different frequencies in the deflectometry, as shown in FIGS. 4 and 5, so as to acquire, through Fourier transform, each wrapped phase by frequency and acquiring unwrapped phases from the 4 wrapped phases. The composite pattern generation part in association with the first embodiment of the present disclosure generates 4 different patterns. The generated patterns are a pattern in a first direction, i.e., a pattern in a vertical direction, a pattern in a second direction, i.e., a pattern in a horizontal direction, a pattern in a third direction rotated 45 degrees in a clockwise direction and a pattern in a fourth direction rotated 45 degrees in an anticlockwise direction. The respective patterns are represented by Formulas 1 to 4 as below.

(20) $\begin{array}{cc}\mathrm{Pattern}\mathrm{in}\mathrm{the}\mathrm{first}\mathrm{direction}& \end{array}$$\begin{array}{cc}{I}_x\left(x,y\right)=\frac{A}{2}\left(1+\cos \left(2\pi \mathrm{fx}\right)\right)& \left[\mathrm{Formula}1\right]\end{array}$$\begin{array}{cc}\mathrm{Pattern}\mathrm{in}\mathrm{the}\mathrm{second}\mathrm{direction}& \end{array}$$\begin{array}{cc}{I}_y\left(x,y\right)=\frac{A}{2}\left(1+\cos \left(2\pi \mathrm{fy}\right)\right)& \left[\mathrm{Formula}2\right]\end{array}$$\begin{array}{cc}\mathrm{Pattern}\mathrm{in}\mathrm{the}\mathrm{third}\mathrm{direction}& \end{array}$$\begin{array}{cc}{I}_{1\mathrm{xy}}\left(x,y\right\}=\frac{A}{2}\left(1+\cos \left[2\pi \left(f+1\right)x+2\pi \mathrm{fy}\right]\right)& \left[\mathrm{Formula}3\right]\end{array}$$\begin{array}{cc}\mathrm{Pattern}\mathrm{in}\mathrm{the}\mathrm{fourth}\mathrm{direction}& \end{array}$$\begin{array}{cc}{I}_{2\mathrm{xy}}\left(x,y\right)=\frac{A}{2}\left(1+\cos \left[2\pi \left(-f\right)x+2\pi \left(f+1\right)y\right]\right)& \left[\mathrm{Formula}4\right]\end{array}$

(21) And as synthesizing the patterns of Formulas 1 to 4, the composite pattern of the following Formula 5 or 6 (S1). FIG. 4 is a view showing a method for generating the composite pattern by synthesizing 4 or more different patterns, by the composite pattern generation part 10 in accordance with the first embodiment of the present disclosure.

(22) $\begin{array}{cc}{I}_{\mathrm{composite}}\left(x,y\right)=\frac{I_x+I_y+I_{1\mathrm{xy}}+I_{2\mathrm{xy}}}{4}& \left[\mathrm{Formula}5\right]\end{array}$$\begin{array}{cc}\mathrm{or},& \end{array}$$\begin{array}{cc}{I}_{\mathrm{compisite}}=\frac{A}{8}\left(4+\cos \left(2\pi \mathrm{fx}\right)+\cos \left(2\pi \mathrm{fy}\right)+\cos \left[2\pi \left(f+1\right)x+2\pi \mathrm{fy}\right]+\cos \left[2\pi \left(-f\right)x+2\pi \left(f-1\right)y\right]\right),& \left[\mathrm{Formula}6\right]\end{array}$

(23) wherein, f represents a frequency to be scanned to the pattern generation part.

(24) And the composite pattern is scanned to the measurement object, this then acquiring an image of the composite pattern reflected through the detector (camera) 20 (S3).

(25) Then, the independent pattern extraction part 31 decomposes, through Fourier transform, the acquired image of the composite pattern into each independent pattern of patterns in the first to fourth directions (S4).

(26) That is, the independent pattern extraction part 31 decomposes, through Fourier transform, the acquired composite pattern into 4 independent patterns. The technical feature of the present application is to use spatial-carrier frequency phase-shifting method (SCFPS) in order to measure, through Fourier transform, phases from the 4 independent patterns. FIG. 5 shows a method for extracting 4 independent patterns from a composite pattern through Fourier transform in association with the first embodiment of the present disclosure. And FIG. 6 is a view showing frequency component analysis of a composite pattern and positions of each filter in the Fourier area in association with the first embodiment of the present disclosure. Further, FIG. 7 shows each shape of filters in the Fourier area for decomposing a composite pattern into 4 patterns in association with the first embodiment of the present disclosure.

(27) This method settles matters of errors at boundaries in Fourier transform method, concurrently with extracting accurate phases using phase-shifting method.
I′.sub.composite(u,v)=A(0,0)+D.sub.x exp(u−f,v)+D*.sub.x exp(u+f,v)+D.sub.y exp(u,v−f)÷D*.sub.y exp(u,v+f)+D.sub.1xy exp(u−f,v−f)+D*.sub.1xy exp(u+f+1,v+f)+D.sub.2xy exp(u−f,v+f+1)+D*.sub.2xy exp(u+f,v−f−1)  [Formula 7]

(28) wherein capital letters represent the respective frequency components in the Fourier area, u and v represent coordinates therein, and f represents a carrier frequency value. At this time, the carrier frequency value, f should be provided with a value large enough to avoid overlapping the respective frequency components. Four filters provided in FIG. 7 are applied to frequency distribution components in the Fourier area of FIG. 6, thus obtaining frequency components of the following Formulas 8 to 11.
Θ.sub.x(u,v)=D.sub.x exp(u−f,v)+D*.sub.x exp(u+f,v)  [Formula 8]
Θ.sub.y(u,v)=D.sub.y exp(u,v−f)+D*.sub.y exp(u,v+f)  [Formula 9]
Θ.sub.1xy(u,v)=D.sub.1xy exp(u−f−1,v−f)+D*.sub.1xy exp(u+f+1,v+f)  [Formula 10]
Θ.sub.2xy(u,v)=D.sub.2xy exp(u−f,v−f−1)+D*.sub.2xy exp(u+f,v+f+1)  [Formula 11]

(29) Further, as taking Fourier transform on the respective frequency components acquired in the above, obtained are signals of the following Formulas 12 to 15.
I.sub.x(x,y)=|FFT.sup.−1(Θ.sub.x(u,v))|  [Formula 12]
I.sub.y(x,y)=|FFT.sup.−1(Θ.sub.y(u,v))|  [Formula 13]
I.sub.1xy(x,y)=|FFT.sup.−1(Θ.sub.1xy(u,v))|  [Formula 14]
I.sub.2xy(x,y)=|FFT.sup.−1(Θ.sub.2xy(u,v))|  [Formula 15]

(30) wherein | | represents the absolute value.

(31) And measured are the wrapped phases through spatial-carrier frequency phase-shifting method (SCFPS). That is, extracted are the wrapped phases of sine patterns decomposed by each frequency through SCFPS method.

(32) The phase acquisition part 30 in accordance with the first embodiment of the present disclosure is constructed to include a regularization part 32 which regularizes the sine patterns for the respective independent patterns extracted by the independent pattern extraction part 31, and a wrapped phase extraction part 33 which extracts the wrapped patterns from the plurality of spatial phase-shifting patterns moved in a pixel unit from the regularized sine patterns.

(33) The regularization part 32 applies Lissajous figure and, Ellipse fitting method to nonregularized sine pattern signals, so as to regularize the sine patterns (S5). That is, used are Lissajous figure and Ellipse fitting method in order to minimize errors promising to occur as the sine patterns are deformed according to external environment and the condition of a measurement specimen when extracting the phases. The sine patterns are regularized through these methods, so as to increase the accuracy of phase extractions. Commonly, the nonregularized sine pattern signals are represented by the following formula 16.
I.sub.x(x,y)=A(x,y)+B(x,y)cos(Φ(x,y))  [Formula 16]

(34) wherein, A(x,y) and B(x,y) represent values for the dimension of the backlight of the sine patterns and for the amplitude thereof. FIG. 8 is a view showing a method for generating Lissajous figure and regularizing patterns, so as to apply spatial-carrier frequency phase-shifting method (SCFPS) in association with the first embodiment of the present disclosure.

(35) As shown in FIG. 8, obtained are 5 values [1, 2, 3, 4, 5] of pixel information from the signal of the nonregularized sine patterns sequentially, then saved in N.sub.i(i=1, 2, 3, 4, 5). As moving one pixel, obtained are N.sub.i and 5 values [2, 3, 4, 5, 6] of pixel information sequentially, then saved in D.sub.i (i=1, 2, 3, 4, 5). Following this, Lissajous figure is generated in which x- and y-axes are as N.sub.i and D.sub.i, respectively. In order to generate the Lissajous figure, required are at least 5 or more measurement values, wherein the accuracy in the measurement becomes increased as much as the number of measurement values, while there is a drawback to take longer time for the calculation. The generated Lissajous figure is represented in an oval shape and as a conic equation of the following formula 17.
C.sub.1.Math.I.sub.1.sup.2+2C.sub.2.Math.I.sub.1I.sub.2+C.sub.3.Math.I.sub.2.sup.2+2C.sub.4.Math.I.sub.1+2C.sub.5.Math.I.sub.2+C.sub.6=0  [Formula 17]

(36) wherein, I.sub.1=N.sub.i, I.sub.2=D.sub.i(C1, C2, C3, C4, C5, C6) being conic constants. (At this time, for the convenience of the equation, C6 is normally provided as −1).

(37) The dimension of the backlight of the sine patterns and the amplitude thereof are calculated by least square fitting method as below.

(38) $\begin{array}{cc}A\left(x,y\right)=\frac{C_2{C}_5-C_3{C}_4}{\alpha },B\left(x,y\right)=\frac{\sqrt{-C_3\Delta }}{\alpha }& \left[\mathrm{Formula}18\right]\end{array}$

(39) wherein, α and Δ are as the following Formula 19.

(40) $\begin{array}{cc}\alpha =.Math.\begin{array}{cc}{C}_1& C_2\\ C_2& C_3\end{array}.Math.,\Delta =.Math.\begin{array}{ccc}{C}_1& C_2& C_4\\ C_2& C_3& C_5\\ C_4& C_5& C_6\end{array}.Math.& \left[\mathrm{Formula}19\right]\end{array}$

(41) And the values for the backlight and the amplitude are acquired, this then potentiating regularization of the sine patterns as below.

(42) $\begin{array}{cc}{\tilde{I}}_x\left(x,y\right)=\frac{I_x\left(x,y\right)-A\left(x,y\right)}{B\left(x,y\right)}& \left[\mathrm{Formula}20\right]\end{array}$

(43) And the wrapped phase extraction part 33 extracts wrapped phases from a plurality of spatial-phase shifting-patterns moved in a pixel unit from the regularized sine patterns (S6). That is, the wrapped phase extraction part 33 obtains the plurality of spatial-phase shifting-patterns moved in a pixel unit for each of the patterns in the first to fourth directions from the regularized sine patterns, obtains phase shifts for each of the spatial-phase shifting-patterns and extracts, therefrom, the wrapped phases for each of the patterns in the first to fourth directions.

(44) Particularly, obtained are 4 spatial-phase shifting-patterns moved in a pixel unit as below from the regularized sine patterns. The pattern in the vertical direction, i.e., the pattern in the first direction is as the following Formulas 21 to 24.
Ĩ.sub.1x(x,y)=Ĩ.sub.x(x,y)=Ã.sub.1x(x,y)+{tilde over (B)}.sub.1x(x,y)cos{Φ.sub.x(x,y)+δ.sub.1x(x,y)}  [Formula 21]
Ĩ.sub.2x(x,y)=Ĩ.sub.x(x+1,y)=Ã.sub.2x(x,y)+{tilde over (B)}.sub.2x(x,y)cos{Φ.sub.x(x,y)+δ.sub.2x(x,y)}  [Formula 22]
Ĩ.sub.3x(x,y)=Ĩ.sub.x(x+2,y)=Ã.sub.3x(x,y)+{tilde over (B)}.sub.3x(x,y)cos{Φ.sub.x(x,y)+δ.sub.3x(x,y)}  [Formula 23]
Ĩ.sub.4x(x,y)=Ĩ.sub.x(x+3,y)=Ã.sub.3x(x,y)+{tilde over (B)}.sub.3x(x,y)cos{Φ.sub.x(x,y)+δ.sub.3x(x,y)}  [Formula 24]

(45) And the pattern in the horizontal direction, i.e., the pattern in the second direction is as the following Formulas 25 to 29.
Ĩ.sub.1y(x,y)=Ĩ.sub.y(x,y)=Ã.sub.1y(x,y)+{tilde over (B)}.sub.1y(x,y)cos{Φ.sub.y(x,y)+δ.sub.1y(x,y)}  [Formula 25]
Ĩ.sub.2y(x,y)=Ĩ.sub.y(x,y+1)=Ã.sub.2y(x,y)+{tilde over (B)}.sub.2y(x,y)cos{Φ.sub.y(x,y)+δ.sub.2y(x,y)}   [Formula 26]
Ĩ.sub.3y(x,y)=Ĩ.sub.y=(x,y+2)Ã.sub.3y(x,y)+{tilde over (B)}.sub.3y(x,y)cos{Φ.sub.y(x,y)+δ.sub.3y(x,y)}   [Formula 27]
Ĩ.sub.4y(x,y)=Ĩ.sub.y(x,y+3)=Ã.sub.4y(x,y)+{tilde over (B)}.sub.4y(x,y)cos{Φ.sub.y(x,y)+δ.sub.4y(x,y)}   [Formula 28]

(46) And the pattern in the third direction rotated 45 degrees in a clockwise direction from the pattern in the horizontal direction is as the following Formulas 29 to 32.
Ĩ.sub.11xy(x,y)=Ĩ.sub.1xy(x,y)=Ã.sub.11xy(x,y)+{tilde over (B)}.sub.11xy(x,y)cos{Φ.sub.1xy(x,y)+δ.sub.11xy(x,y)}  [Formula 29]
Ĩ.sub.21xy(x,y)=Ĩ.sub.1xy(x+1,y)=Ã.sub.21xy(x,y)+{tilde over (B)}.sub.21xy(x,y)cos{Φ.sub.1xy(x,y)+δ.sub.21xy(x,y)}  [Formula 30]
Ĩ.sub.31xy(x,y)=Ĩ.sub.3xy(x,y+1)=Ã.sub.31xy(x,y)+{tilde over (B)}.sub.31xy(x,y)cos{Φ.sub.1xy(x,y)+δ.sub.31xy(x,y)}  [Formula 31]
Ĩ.sub.41xy(x,y)=Ĩ.sub.1xy(x+1,y+1)=Ã.sub.41xy(x,y)+{tilde over (B)}.sub.41xy(x,y)cos{Φ.sub.1xy(x,y)+δ.sub.41xy(x,y)}  [Formula 32]

(47) And the pattern in the fourth direction rotated 45 degrees in an counterclockwise direction from the pattern in the horizontal direction is as the following Formulas 33 to 36.
Ĩ.sub.12xy(x,y)=Ĩ.sub.2xy(x,y)=Ã.sub.12xy(x,y)+{tilde over (B)}.sub.12xy(x,y)cos{Φ.sub.2xy(x,y)+δ.sub.12xy(x,y)}  [Formula 33]
Ĩ.sub.22xy(x,y)=Ĩ.sub.2xy(x+1,y)=Ã.sub.22xy(x,y)+{tilde over (B)}.sub.22xy(x,y)cos{Φ.sub.2xy(x,y)+δ.sub.22xy(x,y)}  [Formula 34]
Ĩ.sub.32xy(x,y)=Ĩ.sub.2xy(x,y+1)=Ã.sub.32xy(x,y)+{tilde over (B)}.sub.32xy(x,y)cos{Φ.sub.2xy(x,y)+δ.sub.32xy(x,y)}  [Formula 35]
Ĩ.sub.42xy(x,y)=Ĩ.sub.2xy(x+1,y+1)=Ã.sub.42xy(x,y)+{tilde over (B)}.sub.42xy(x,y)cos{Φ.sub.2xy(x,y)+δ.sub.42xy(x,y)}  [Formula 36]

(48) And a method for extracting the wrapped phases from the aforementioned spatial-phase shifting-patterns is as below. The patterns in the vertical direction, for example, are as below. Firstly, the regularized pattern in the vertical direction, i.e., the pattern in the first direction is represented by the following Formula 37.
Ĩ.sub.x(x,y)=Ã.sub.x(x,y)+{tilde over (B)}.sub.x(x,y)cos{Φ.sub.x(x,y)}  [Formula 37]

(49) wherein, in the right-hand side, a first value represents regularized backlight and a second value represents regularized amplitude. Thus, in theory, the first value is 0 and the second value is 1.

(50) In fact, the first and second values are changed in the sine patterns due to external noises, however being supposed as the following Formula 38 in 4 adjacent pixels.

(51) $\begin{array}{cc}\{\begin{array}{c}{\tilde{A}}_x\left(x,y\right)\approx {\tilde{A}}_{1x}\left(x,y\right)\approx {\tilde{A}}_{2x}\left(x,y\right)\approx {\tilde{A}}_{3x}\left(x,y\right)\approx {\tilde{A}}_{4x}\left(x,y\right)\\ {\tilde{B}}_x\left(x,y\right)\approx {\tilde{B}}_{1x}\left(x,y\right)\approx {\tilde{B}}_{2x}\left(x,y\right)\approx {\tilde{B}}_{3x}\left(x,y\right)\approx {\tilde{B}}_{4x}\left(x,y\right)\end{array}& \left[\mathrm{Formula}38\right]\end{array}$

(52) A method for obtaining the phases from the patterns in the vertical direction represented by Formulas 21 and 24 is as below. The phase shifts may be the same or different in each pixel, however, Fourier transform method or least square iterative method is performed in order to compensate the phase shifts changed due to external vibrations and noises. In accordance with the first embodiment of the present disclosure, described is the method for obtaining the phase shifts through Fourier transform and obtaining the phases therefrom. The pattern in the vertical direction represented by Formula 21 is Fourier transformed, this then being represented as the following Formula 39.
Ĩ.sub.1x(u,v)=a.sub.1x(u,v)+d.sub.1x exp(u−f,v)+d*.sub.1x exp(u+f,f)  [Formula 39]

(53) And only a specific frequency, an f component is obtained through a filter and then is inverse Fourier transformed, this then being as the following Formula 40.
D.sub.1x(x,y)=FFT.sup.−1[d.sub.1x(u,v)]  [Formula 40]

(54) Then, the phase of Ĩ.sub.1x(x,y) is provided as the following Formula 41.

(55) $\begin{array}{cc}{\phi }_{1x}\left(x,y\right)=\mathrm{wrap}\left[{\Phi }_x\left(x,y\right)+{\delta }_{1x}\left(x,y\right)\right]={\tan }^{-1}\left(\frac{\mathrm{imag}\left[D_{1x}\left(x,y\right)\right]}{\mathrm{real}\left[D_{1x}\left(x,y\right)\right]}\right)& \left[\mathrm{Formula}41\right]\end{array}$

(56) Similarly, the phase of Ĩ.sub.2x(x,y), Ĩ.sub.3x(x,y), Ĩ.sub.4x(x,y) is produced as the following Formulas 42 to 44.
φ.sub.2x(x,y)=wrap[Φ.sub.x(x,y)+δ.sub.2x(x,y)]  [Formula 42]
φ.sub.3x(x,y)=wrap[Φ.sub.x(x,y)+δ.sub.3x(x,y)]  [Formula 43]
φ.sub.4x(x,y)=wrap[Φ.sub.x(x,y)+δ.sub.4x(x,y)]  [Formula 44]

(57) And the respective phase shifts are provided from the acquired phases as the following Formulas 45 to 48.
δ.sub.1x(x,y)=0  [Formula 45]
δ.sub.2x(x,y)=unwrap[φ.sub.2x(x,y)]−unwrap[φ.sub.1x(x,y)]  [Formula 46]
δ.sub.3x(x,y)=unwrap[φ.sub.3x(x,y)]−unwrap[φ.sub.1x(x,y)]  [Formula 47]
δ.sub.4x(x,y)=unwrap[φ.sub.4x(x,y)]−unwrap[φ.sub.1x(x,y)]  [Formula 48]

(58) And each of the acquired phase shifts are input into the repeated least square algorithm, so as to provide phase values for the respective patterns as below. The patterns in the vertical direction represented by from Formula 21 to Formula 24 are represented by the following Formula 49.
Ĩ.sub.nx(x,y)=Ã.sub.x(x,y)+E(x,y)cos(δ.sub.nx(x,y))+F(x,y)sin(δ.sub.nx(x,y))  [Formula 49]
wherein,
E(x,y)={tilde over (B)}.sub.x(x,y)cos(Φ.sub.x(x,y))
F(x,y)=−{tilde over (B)}.sub.x(x,y)sin(Φ.sub.x(x,y))

(59) According to the least square algorithm, it is only to obtain a phase value at the time when an error value represented by the following Formula 50 becomes minimum.

(60) $\begin{array}{cc}S\left(x,y\right)=\underset{n=1}{\overset{N}{.Math.}}{\left({\tilde{I}}_{\mathrm{nx}}^e\left(x,y\right)-{\tilde{I}}_{\mathrm{nx}}\left(x,y\right)\right)}^2& \left[\mathrm{Formula}50\right]\end{array}$

(61) wherein Ĩ.sub.nx.sup.e(x,y) is a regularized pattern value obtained through tests, and N represents the number of the whole patterns acquired. The phase value satisfies the following condition when Formula 50 becomes minimum.

(62) $\begin{array}{cc}\frac{\partial S\left(x,y\right)}{\partial A_x\left(x,y\right)}=0,\frac{\partial S\left(x,y\right)}{\partial E\left(x,y\right)}=0,\frac{\partial S\left(x,y\right)}{\partial F\left(x,y\right)}=0& \left[\mathrm{Formula}51\right]\end{array}$

(63) And the above Formula 51 is represented as below.

(64) 0$\begin{array}{cc}\mathrm{PX}=Q& \left[\mathrm{Formula}52\right]\end{array}$$\begin{array}{cc}\mathrm{wherein},& \end{array}$$\begin{array}{cc}P=\left[\begin{array}{ccc}N& \underset{n=1}{\overset{N}{.Math.}}\cos {\delta }_{\mathrm{nx}}& \underset{n=1}{\overset{N}{.Math.}}\sin {\delta }_{\mathrm{nx}}\\ \underset{n=1}{\overset{N}{.Math.}}\cos {\delta }_{\mathrm{nx}}& \underset{n=1}{\overset{N}{.Math.}}{\cos }^2{\delta }_{\mathrm{nx}}& \underset{n=1}{\overset{N}{.Math.}}\cos {\delta }_{\mathrm{nx}}\sin {\delta }_{\mathrm{nx}}\\ \underset{n=1}{\overset{N}{.Math.}}\sin {\delta }_{\mathrm{nx}}& \underset{n=1}{\overset{N}{.Math.}}\sin {\delta }_{\mathrm{nx}}\cos {\delta }_{\mathrm{nx}}x& \underset{n=1}{\overset{N}{.Math.}}{\sin }^2{\delta }_{\mathrm{nx}}\end{array}\right]& \left[\mathrm{Formula}53\right]\end{array}$$\begin{array}{cc}Q={\left[\begin{array}{ccc}\underset{n=1}{\overset{N}{.Math.}}{\tilde{I}}_{\mathrm{nx}}\left(x,y\right)& \underset{n=1}{\overset{N}{.Math.}}{\tilde{I}}_{\mathrm{nx}}\left(x,y\right)\cos {\delta }_n& \underset{n=1}{\overset{N}{.Math.}}{\tilde{I}}_{\mathrm{nx}}\left(x,y\right)\sin {\delta }_n\end{array}\right]}^T& \left[\mathrm{Formula}54\right]\end{array}$$\begin{array}{cc}X={\left[\begin{array}{ccc}{\tilde{A}}_x\left(x,y\right)& E\left(x,y\right)& F\left(x,y\right)\end{array}\right]}^T& \left[\mathrm{Formula}55\right]\end{array}$

(65) wherein, δ.sub.nx(x,y) is simply represented as δ.sub.nx.

(66) The phase is provided from the pattern I.sub.x(x,y) by using E(x,y) and F(x,y) acquired in the above, being as the following Formula 56.

(67) $\begin{array}{cc}{\Phi }_{\mathrm{wx}}\left(x,y\right)={\tan }^{-1}\left\{\frac{-E\left(x,y\right)}{F\left(x,y\right)}\right\}& \left[\mathrm{Formula}56\right]\end{array}$

(68) Similarly, the phase values Φ.sub.wy(x,y), Φ.sub.w1xy(x,y), Φ.sub.w2xy(x,y) by a pattern are provided from the respective patterns, I.sub.y(x,y), I.sub.1xy(x,y), I.sub.2xy(x,y).

(69) And the phase acquisition part 30 in association with the first embodiment of the present disclosure includes the unwrapped phase acquisition part 34, and the unwrapped phase acquisition part 34 obtains one cycle of phases for the pattern in the first direction and the pattern in the second direction, so as to acquire the unwrapped phases for the pattern in the first direction and the pattern in the second direction (S7).

(70) That is, the unwrapped phases can be calculated, through the method as below, from the 4 unwrapped phases acquired. Like the undermost Formulas 57 and 58, obtained are one cycle of phases for the pattern in the vertical direction, i.e., the pattern in the first direction and the pattern in the horizontal direction, i.e., the pattern in the second direction.
θ.sub.x(x,y)=wrapToPi[Φ.sub.w1xy(x,y)−Φ.sub.wx(x,y)−Φ.sub.wy(x,y)]  [Formula 57]
θ.sub.y(x,y)=wrapToPi[Φ.sub.w2xy(x,y)+Φ.sub.wx(x,y)−Φ.sub.wy(x,y)]  [Formula 58]

(71) wherein, wrapToPi is a conversion operator which reconstructs the phase value in the range of [−π, π], being represented as below.
wrapToPi[α]=mod(α+π,2π)−π  [Formula 59]

(72) wherein, “mod” means a remainder following the division by 2π. Then, the unwrapped phases for the patterns in the vertical and horizontal directions are provided as the following formulas 60 and 61.

(73) $\begin{array}{cc}{\Phi }_x\left(x,y\right)=\mathrm{round}\left[\frac{{\theta }_x\left(x,y\right)f-{\Phi }_{\mathrm{wx}}\left(x,y\right)}{2\pi }\right]2\pi +{\Phi }_{\mathrm{wx}}\left(x,y\right)& \left[\mathrm{Formula}60\right]\\ {\Phi }_y\left(x,y\right)=\mathrm{round}\left[\frac{{\theta }_y\left(x,y\right)f-{\Phi }_{\mathrm{wy}}\left(x,y\right)}{2\pi }\right]2\pi +{\Phi }_{\mathrm{wy}}\left(x,y\right)& \left[\mathrm{Formula}61\right]\end{array}$

(74) And the analyzing means 40 measures and analyzes the 3D shape of the measurement object from the acquired phases (S8).

(75) Hereinafter, described is a method for profile measurement based on high-speed deflectometry using composite patterns in association with a second embodiment of the present disclosure. Firstly, FIG. 9 is a flow chart of a method for profile measurement based on high-speed deflectometry using composite patterns in association with the second embodiment of the present disclosure. And FIG. 10 is a flow chart for acquiring unwrapped phases using spatial-carrier frequency phase-shifting method (SCFPS) in 3 composite patterns having different frequencies in association with the second embodiment of the present disclosure.

(76) As shown in FIGS. 10 and 11, similarly to the first embodiment, in the second embodiment of the present disclosure, generated are a plurality of composite patterns having different frequencies for composite patterns generated by synthesizing a pattern in a vertical direction, i.e., a pattern in a first direction and a pattern in a horizontal direction, i.e., a pattern in a second direction (S10), this then being scanned to a measurement object (S20). A detector 20 acquires these reflected composite patterns (S30), a phase acquisition 30 part extracts each of the patterns in the first and second directions for the plurality of composite patterns, independently (S40), followed by regularization (S50). Following extracting a plurality of wrapped phases for each of the patterns in the first and second directions (S60), acquired are unwrapped phases from the wrapped phases of the plurality of the patterns in the first direction and unwrapped phases from the wrapped phases of the plurality of the patterns in the second direction (S70). And the shape of the measurement object is analyzed based on the acquired unwrapped phases (S80).

(77) Particularly, first, a composite pattern generation part generates composite patterns using different frequencies. The composite patterns are represented by the sum of the pattern in the vertical direction, i.e., the pattern in the first direction and the pattern in the horizontal direction i.e., the pattern in the second direction, and forms a number of the composite patterns having different frequencies. If the number of the composite patterns is small, the time for measurement thereof would be shortened while decreasing a measurement accuracy. On the other hand, if the number of the composite patterns is large, the time for measurement thereof would be longer while increasing a measurement accuracy. Commonly, the composite patterns are represented as the following Formula 62.

(78) $\begin{array}{cc}{I}_0\left(x,y\right)=\frac{G}{4}\left(2+\cos \left(2\pi f_{0}x\right)+\cos \left(2\pi f_{0}x\right)\right)& \left[\mathrm{Formula}62\right]\end{array}$

(79) And the rest of the composite patterns are represented as the following Formulas 63 and 64.

(80) $\begin{array}{cc}{I}_n\left(x,y\right)=\frac{G}{4}\left[2+\cos \left(2\pi f_{n}x\right)+\cos \left(2\pi f_{n}y\right)\right]& \left[\mathrm{Formula}63\right]\\ f_i=f_0-{\left(f_0\right)}^{\left(i-1\right)\setminus /\left(N-1\right)},1\le i\le N& \left[\mathrm{Formula}64\right]\end{array}$

(81) wherein, 1≤n≤N, N=3, 4, 5. N is the number of the composite patterns.

(82) And a number of the composite patterns are scanned to the measurement object, and the detector 20 measures the shape of the reflected composite patterns.

(83) FIG. 11 shows a method for extracting independent patterns in the first and second directions from a composite pattern through Fourier transform, by an independent pattern extraction part 31 in association with the second embodiment of the present disclosure. As shown in FIG. 11, the measured composite pattern is decomposed, through Fourier transform, into patterns in the vertical and horizontal directions concurrently with removing noise components due to the external noises. The Fourier transformed composite pattern is represented as the following Formula 65.
I(u,v)=A.sub.0(u,v)+B.sub.x exp(u−f,v)+B*.sub.x exp(u+f,v)+B.sub.y exp(u,v−f)+B*.sub.y exp(u,v+f)  [Formula 65]

(84) In Formula 65, x and y frequency components are decomposed, then being represented by the following Formulas 66 and 67.
Θ.sub.0x(u,v)=B.sub.x exp(u−f,v)+B*.sub.x exp(u+f,v)  [Formula 66]
Θ.sub.0y(u,v)=B.sub.y exp(u−f,v)+B*.sub.y exp(u+f,v)  [Formula 67]

(85) And the respective patterns in the vertical direction (x-direction) and horizontal direction (y-direction) are decomposed through inverse Fourier transform, this then potentiating reconstruction thereof. In the same manner, as applying Fourier transform to a number of the composite patterns, acquired are the patterns for the vertical and horizontal directions as the following Formula 68.

(86) $\begin{array}{cc}\hspace{1em}\{\begin{array}{c}{X}_n\left(x,y\right)=.Math.{\mathrm{FFT}}^{-1}\left({\Theta }_{\mathrm{nx}}\left(u,v\right)\right).Math.\\ Y_n\left(x,y\right)=.Math.{\mathrm{FFT}}^{-1}\left({\Theta }_{\mathrm{ny}}\left(u,v\right)\right).Math.\end{array},0\le n\le N& \left[\mathrm{Formula}68\right]\end{array}$

(87) And the wrapped phases by each pattern are provided through the aforesaid spatial-carrier frequency phase-shifting method. That is, phase values, Φ.sub.nwx(x,y) and Φ.sub.nwy(x,y) are obtained from the patterns of X.sub.n(x,y) and Y.sub.n(x,y).

(88) And a method for acquiring unwrapped phases from wrapped phases is as below. Since the same procedures are proceeded in both of the patterns in the vertical direction (x-direction) and horizontal direction (y-direction), it is described only for the vertical direction.

(89) At the very beginning, a phase difference between the highest frequency component and a frequency component lower than this is obtained as the following Formula 69. For reference, when n=0, the highest frequency component is provided.
θ.sub.x,n-0=wrapToPi[Φ.sub.nvx(x,y)−Φ.sub.0wx(x,y)]  [Formula 69]

(90) 1≤n≤N (N is the number of the used composite patterns, 3≤N≤5)

(91) wrapToPi is an operator as defined in the above.

(92) Described are roughly 3 cases according to the number of the used composite patterns.

(93) Case 1: using 3 composite patterns (N=3)

(94) Step 1: performing phase unwrapping of θ.sub.x,2-0, using θ.sub.x,1-0, as the following Formula 70.

(95) $\begin{array}{cc}{\theta }_{\mathrm{ux},2-0}=\mathrm{round}\left[\frac{{\theta }_{x,1-0}\left(x,y\right)\left(f_0-f_2\right)/\left(f_0-f_1\right)-{\theta }_{x,2-0}\left(x,y\right)}{2\pi }\right]2\pi +{\theta }_{x,2-0}\left(x,y\right)& \left[\mathrm{Formula}70\right]\end{array}$

(96) Step 2: performing phase unwrapping of Φ.sub.0wx, using θ.sub.ux,2-0, as the following Formula 71, so as to obtain phases.

(97) $\begin{array}{cc}{\Phi }_{0x}=\mathrm{round}\left[\frac{{\theta }_{\mathrm{ux},2-0}\left(x,y\right)\left(f_0-f_2\right)-{\Phi }_{0\mathrm{wx}}\left(x,y\right)}{2\pi }\right]2\pi +{\Phi }_{0\mathrm{wx}}\left(x,y\right)& \left[\mathrm{Formula}71\right]\end{array}$

(98) Case 2: using 4 composite patterns (N=4)

(99) Step 1: performing phase unwrapping of θ.sub.x,2-0, using θ.sub.x,1-0, as the following Formula 72.

(100) $\begin{array}{cc}{\theta }_{\mathrm{ux},2-0}=\mathrm{round}\left[\frac{\begin{array}{c}{\theta }_{x,1-0}\left(x,y\right)\left(f_0-f_2\right)/\\ \left(f_0-f_1\right)-{\theta }_{x,2-0}\left(x,y\right)\end{array}}{2\pi }\right]2\pi +{\theta }_{x,2-0}\left(x,y\right)& \left[\mathrm{Formula}72\right]\end{array}$

(101) Step 2: performing phase unwrapping of θ.sub.x,3-0, using the phase values acquired in Formula 72, as the following Formula 73.

(102) $\begin{array}{cc}{\theta }_{\mathrm{ux},3-0}=\mathrm{round}[\frac{\begin{array}{c}{\theta }_{\mathrm{ux},2-0}\left(x,y\right)\left(f_0-f_3\right)/\\ \left(f_0-f_2\right)-{\theta }_{x,3-0}\left(x,y\right)\end{array}}{2\pi }]2\pi \hspace{1em}+{\theta }_{x,3-0}\left(x,y\right)& \left[\mathrm{Formula}73\right]\end{array}$

(103) Step 3: performing phase unwrapping of Φ.sub.0wx, using θ.sub.ux,3-0, as the following Formula 74, so as to obtain phases.

(104) 0$\begin{array}{cc}{\Phi }_{0x}=\mathrm{round}\left[\frac{{\theta }_{\mathrm{ux},3-0}\left(x,y\right)\left(f_0-f_3\right)-{\Phi }_{0\mathrm{wx}}\left(x,y\right)}{2\pi }\right]2\pi +{\Phi }_{0\mathrm{wx}}\left(x,y\right)& \left[\mathrm{Formula}74\right]\end{array}$

(105) Case 3: using 5 composite patterns (N=5)

(106) Step 1: performing phase unwrapping of θ.sub.x,2-0, using θ.sub.x,1-0, as the following Formula 75.

(107) $\begin{array}{cc}{\theta }_{\mathrm{ux},2-0}=\mathrm{round}[\frac{\begin{array}{c}{\theta }_{x,1-0}\left(x,y\right)\left(f_0-f_2\right)/\\ \left(f_0-f_2\right)-{\theta }_{x,2-0}\left(x,y\right)\end{array}}{2\pi }]2\pi \hspace{1em}+{\theta }_{x,2-0}\left(x,y\right)& \left[\mathrm{Formula}75\right]\end{array}$

(108) Step 2: performing phase unwrapping of θ.sub.x,3-0, using the phase values acquired in Formula 75, as the following Formula 76.

(109) $\begin{array}{cc}{\theta }_{\mathrm{ux},3-0}=\mathrm{round}[\frac{\begin{array}{c}{\theta }_{\mathrm{ux},2-0}\left(x,y\right)\left(f_0-f_3\right)/\\ \left(f_0-f_2\right)-{\theta }_{x,3-0}\left(x,y\right)\end{array}}{2\pi }]2\pi \hspace{1em}+{\theta }_{x,3-0}\left(x,y\right)& \left[\mathrm{Formula}76\right]\end{array}$

(110) Step 3: performing phase unwrapping of θ.sub.x,4-0, using the phase values acquired in Formula 76, as the following Formula 77.

(111) $\begin{array}{cc}{\theta }_{\mathrm{ux},4-0}=\mathrm{round}[\frac{\begin{array}{c}{\theta }_{\mathrm{ux},3-0}\left(x,y\right)\left(f_0-f_4\right)/\\ \left(f_0-f_3\right)-{\theta }_{x,4-0}\left(x,y\right)\end{array}}{2\pi }]2\pi \hspace{1em}+{\theta }_{x,4-0}\left(x,y\right)& \left[\mathrm{Formu}\mathrm{la}77\right]\end{array}$

(112) Step 4: performing phase unwrapping of Φ.sub.0wx, using θ.sub.ux,4-0, as the following Formula 78, so as to obtain phases.

(113) $\begin{array}{cc}{\Phi }_{0x}=\mathrm{round}[\frac{{\theta }_{\mathrm{ux},4-0}\left(x,y\right)\left(f_0-f_4\right)-{\Phi }_{0\mathrm{wx}}\left(x,y\right)}{2\pi }]2\pi \hspace{1em}+{\Phi }_{0\mathrm{wx}}\left(x,y\right)& \left[\mathrm{Formula}78\right]\end{array}$

(114) As using the aforementioned methods, in the same manner, phase (Φ.sub.0y(x,y) for the pattern in the horizontal direction (y-direction pattern) is also acquired as the following Formula 79.

(115) $\begin{array}{cc}\{\begin{array}{c}{\Phi }_x\left(x,y\right)={\Phi }_{0x}\left(x,y\right)\\ {\Phi }_y\left(x,y\right)={\Phi }_{0y}\left(x,y\right)\end{array}& \left[\mathrm{Formula}79\right]\end{array}$

(116) The phases in the vertical and horizontal directions as described in the above are adopted to the deflectometry, so as to potentiate the real-time measurement of measurement objects having various shapes, such as freeform surfaces.