# The method of optical measurement of the surface shape of a three-dimensional object

The invention relates to the topography, profilometry. The invention consists in the fact that the original object light on an arbitrarily selected first direction of the light beam, the spatial intensity distribution of which in the plane perpendicular to the optical axis of the beam is changed by a given periodic law. In the second direction, different from the first and coincident with an optical axis showing an optical system, registering the first image. Replace the original object with the object with the base flat surface, cover it with the same radiation in the first direction and the second direction register the second image. The original object is additionally light in the first direction by the light beam, the spatial intensity distribution of which in the plane perpendicular to the optical axis of the beam, uniformly, and in the second direction register third image of the object representing a halftone image of the original object. On the third image to form a fourth representing dogradation image of the original object, consisting of white areas and black areas. Synthesize the fifth izobrazhennyh areas of the fourth image. To recover the surface shape of the original three-dimensional object perform joint processing of the fifth and second images. Technical result: the measurement of the surface shape of any complex object with a simultaneous increase measurement accuracy. 8 Il. The present invention relates to the topography, profilometry, in particular non-contact methods of measuring the surface shape of complex three-dimensional objects using optical radiation, and can be used in engineering, medicine, dentistry, forensic medical examination.The known method for the optical measurement of the surface shape of a three-dimensional object, described in the article by J.-F. Lin, X.-Y. Su "Two-dimensional Fourier transform profilometry for the automatic measurement of three-dimensional object shapes", Optical Engineering, Vol. 34, No.11, PP.3297-3302, 1995. The method consists in the fact that the original three-dimensional object light in randomly selected 1-d direction of the light beam, the spatial intensity distribution of which in the plane perpendicular to the optical axis of the beam is changed by a given periodic law. For 2-d direction, different from the 1st and coincident with an optical axis showing an optical system log 1-e subregionalization intensity of the illuminating beam. Then replace the original three-dimensional object with flat surface, the transverse dimensions of which exceed the dimensions of the illuminating beam and the normal to this surface lies in a plane passing through the optical axis of the illuminating beam and the reflecting optical system, and illustrate a flat surface the same radiation at the selected 1-d direction. For 2-d direction register 2nd image whose brightness is proportional to the spatial intensity distribution of the illuminating beam in the object plane. The obtained images are used for further restoration of the surface shape of the original three-dimensional object.The essence of the future restoration of the form is as follows. Let the spatial intensity distribution of the illuminating light beam in the plane perpendicular to the optical axis of the beam is changed according to the harmonic law, for example, it can be represented in the form of a lattice of straight parallel bands, the intensity of which is perpendicular to the direction described by a sinusoidal function. As the 2nd register image is different from the 1st of the directions of projection bands, streaks in the image due to paralo the shape of the surface is encoded in the deviation bands that is, in the shear bands.The main steps of the computational procedure of the processing of the received images and restore them surface profile are listed below. Separately on the 1st and 2nd images perform the following operations.1. Perform the Fourier transform (one-dimensional or two-dimensional). As the brightness of the image modulated by a periodic (sinusoidal) law, their spatial Fourier spectrum will have pronounced peaks (in optics - order diffraction) near spatial frequencies that are multiples of the modulation frequency.2. Allocate +1 (or-1) the order of the Fourier spectrum of an image using band-pass frequency filter.3. Perform inverse Fourier transform on the selected plot the Fourier spectrum with the formation of a complex image.Then perform joint processing of complex images obtained from the 1st and 2nd images. This processing produces consistently for each point of the image, and it consists in the multiplication of 1 and a complex conjugate of the 2nd integrated images, logarithmically received a new integrated image and allocate it the imaginary part. As a result of operations Vosstania Akhmerova of the object relative to a flat surface.The main disadvantage of this method lies in the substantial restriction of the class of investigated objects. This is due to the following.For successful operation the procedure described above for the recovery of the object's shape and improve the accuracy of reconstruction of the surface profile is necessary that all parts of the object was sufficiently large number of bands. This is necessary in order spectrum near1st diffraction orders do not overlap with the range of zero order. The distance between the 0-m and1st orders in the frequency domain is determined by the frequency of the grating (or the period of the stripes). Better separation of the diffraction orders can be achieved by increasing the frequency of the lattice. However, the spatial frequency cannot grow to infinity. Its upper limit is limited by the spatial resolution optical and digital image processing. At the present time for registration and image input computers are mainly used a CCD camera. The most widespread standard television CCD having about h cells (pixels). As for the correct transfer of a single period sinusoidal grating tre is the value and limits the practical maximum number of bands, which you can design on the object. Usually reflecting optical system (the parameters of the lenses) be selected so that the image of the object fills the frame. In this case, the object will be about 70 bands. If the object or part thereof occupy a smaller area of the frame, they have fewer bands. From practice it is known that a good separation of the 0-th and1st diffraction orders can be obtained by having at least 30-35 lines on the object. Therefore, in all parts of the image object should be not less than 35 bands. Because the total number of bands in the frame may not exceed 70 pages, then this means that the object may not have plots, the width of which is less than half of the frame. This condition severely limits the class of the studied objects. As a rule, are investigated objects on any underlying surface type of bas-reliefs, which occupy the entire frame. However, this narrow class of objects. Often it is necessary to measure the three-dimensional surface and three-dimensional objects, which have to rotate the object, to measure the shape of the surface from different angles. In this case, the image of the object will occupy part of the frame, and the remaining area of the frame is dark.For such objects also have ograniczenia object will be populated by a small number of bands. Range of images from these narrow sections will be wide and it will overlap with the zero order. Accordingly, these portions of the object will be restored with distortion, that is, with less accuracy.The present of the invention is to provide a method for optical measurement of the surface shape of a three-dimensional object that provides due to the formation of additional images good separation orders of magnitude in the spectrum of images that allows you to use the proposed method for all types of objects with increasing measurement accuracy.The problem is solved in that in the method of optical measurement of the surface shape of a three-dimensional object, which consists in the fact that the original three-dimensional object light on an arbitrarily selected first direction of the light beam, the spatial intensity distribution of which in the plane perpendicular to the optical axis of the beam is changed by a given periodic law, and in the second direction, different from the first and coincident with an optical axis showing an optical system, registering the first image of the object, which is a grayscale image source trahms the original three-dimensional object with flat base surface, the transverse dimensions of which exceed the dimensions of the illuminating beam and the normal to this surface lies in a plane passing through the optical axis of the illuminating beam and the reflecting optical system that illuminates the object with the base flat surface of the same radiation in a selected first direction and the second direction register the second image whose brightness is proportional to the spatial intensity distribution of the illuminating beam in the object plane with the base flat surface, the obtained images are used for further recovery of the surface shape of the original three-dimensional object, according to the invention of the original three-dimensional object optional light in the first direction by the light beam, the spatial intensity distribution of which in the plane perpendicular to the optical axis of the beam, uniformly, and in the second direction register a third image of the object, which is a grayscale image of the original three-dimensional object obtained by the third image to form a fourth image that represents dogradation image of the original three-dimensional object, consisting of a white beard below the specified level, synthesize the fifth picture, coinciding with the first image in the white areas of the fourth image and the second image in the black areas of the fourth image, and to restore the surface shape of the original three-dimensional object perform joint processing of the fifth and second images.In the proposed method, due to the formation of additional 3rd images are dogradation 4th image and define the boundaries of the original three-dimensional object. Outside these limits the image of the original object complement of the image of the object with the base flat surface. As a result of these operations synthesize 5-th image, which has a striped structure across the frame. This leads to the fact that the range of such images will have a distinct narrow orders, which can easily be separated from the zero order and, accordingly, to improve the accuracy of the recovery profile.Further, the invention is illustrated specific embodiments thereof and the attached drawings, in which: Fig.1 depicts an example of the 1st image of the original three-dimensional object in the form of a ball, modulated striped structure; Fig. 2 is an example of the 2nd image volume of the object image in the form of a ball; Fig.4 - dogradation the image of the object in the form of a ball; Fig.5 is an example of the 5-th image of the original three-dimensional object in the form of a ball, complemented by a striped structure outside the bounds of the object; Fig. 6 is a characteristic graph of a one-dimensional Fourier spectrum of the image of the object modulated striped structure; Fig. 7 is a graph +1-th order Fourier spectrum of the object image in the form of narrow stairs"; Fig. 8 is a graph +1-th order Fourier spectrum of the object image in the form of narrow stairs" with the addition of her striped structure.The proposed method for optical measurement of the surface shape of a three-dimensional object is as follows.The original three-dimensional object light in randomly selected 1-d direction of the light beam, the spatial intensity distribution of which in the plane perpendicular to the optical axis of the beam is changed by a given periodic law. Choose, for example, the harmonic law. For 2-d direction, different from the 1st and coincident with an optical axis showing an optical system, register the 1st image of the object, which is a grayscale image of the original three-dimensional object, modulated by the spatial distribution and the expression can be described by the following expression: i

_{1}(x, y)=a(x, y)+b(x, y)cos[u

_{0}x+f

_{1}(x, y)], (1),

where a is the amplitude of the background, b - vidnosti bands, u

_{0}- frequency bands, f

_{1}- search function (phase), which is associated with the profile of the surface relief. When this record is the spatial intensity distribution of the illuminating beam is a striped structure (lattice), the strokes of which is oriented along the vertical axis, perpendicular to the x axis. An example of such an image for the object in the form of a ball, is shown in Fig.1.Then replace the original three-dimensional object with flat base surface, the transverse dimensions of which exceed the dimensions of the illuminating beam and the normal to this surface lies in a plane passing through the optical axis of the illuminating beam and the reflecting optical system that illuminates the object with the base flat surface of the same radiation in the selected 1-d direction, and 2-d direction register 2nd image whose brightness is proportional to the spatial intensity distribution of the illuminating beam in the object plane with the base flat surface. The second image shown in Fig.2 is an image strips on a flat screen, which is also a bit distorted, as illuminating and tensively 2nd image can be described by a similar expression

i

_{2}(x, y)=a(x, y)+b(x, y)cos[u

_{0}x+f

_{2}(x, y)], (2),

where f

_{2}function, which is associated with aberrations of the optical system.Advanced light source three-dimensional object on the 1st direction of the light beam, the spatial intensity distribution of which in the plane perpendicular to the optical axis of the beam, uniformly, and on 2-d direction register 3-d image of the object (see Fig.3). This is the 3rd image is a grayscale image of the object. This image does not contain striped patterns and it is necessary to obtain the 4th image, which is dogradation (binary) image of the object, consisting of white areas where the brightness exceeds a predefined level, and the black regions in which the brightness below the same level. This image is shown in Fig.4. The threshold level is chosen by the operator, for each image will have its own. Received 4th picture is necessary to obtain the boundary of the image object.After the above operations perform the main operation of the proposed method - synthesize 5-th image, coinciding with the 1st image in the white areas of the 4-th image and the R operations original 1st image of the object (Fig.1) will be complemented by a striped structure (grating) on all the dark areas and accordingly, the number of bands on the entire frame will be equally great. So as to restore the shape of the surface of the original three-dimensional object perform joint processing of the 5-th and 2-th image, the quality of recovery is increased.For proof of this fact refer to a specific example.For further clarification conveniently summarizes the expression be rewritten in the following form:

i

_{1,2}(x, y)=a(x, y)+c

_{1,2}(x, y)exp(ju

_{0}x)+c

_{1,2}*(x, y)exp(-ju

_{0}x), (3),

where

c

_{1,2}(x, y)=0.5 b(x, y)exp[jf

_{1,2}(x, y)], (4),

j is the complex unit, * icon complex conjugation.Separately on the 1st and 2nd images to perform the following operations.1. Compute the Fourier transform of the image (1):

I

_{1,2}(u, v)=A(u, v)+C

_{1,2}(u-u

_{0}, v)+C

_{1,2}*(-u-u

_{0}, v), (5),

where: capital letters marked Fourier images of the respective functions shown above lowercase u, v - frequency coordinates of the spatial coordinates x, y. From (5) we see that at sufficiently high frequency lattice u

_{0}range 1-th image consists of three separate parts corresponding to each term in (5). Moreover, the rst term A(u, v) describes the spectrum near the n-1-th order Fourier spectrum. The characteristic graph of the one-dimensional Fourier spectrum of the image type (1) shown in Fig.6.From (4) it follows that the Fourier spectrum of the +1st order is described by the following function:

C

_{1}(u,v) = 0.5 B(u,v)J[expjf

_{1}(x,y)], (6)

where B(u, v) is the Fourier transform of vidnosti bands b(x, y),icon convolution,[.] - the operation of the direct Fourier transform.2. Allocate +1 (or-1) the order of the Fourier spectrum of an image using band-pass frequency filter. Mathematically this means that from the expression (5) leave, for example, only the second term C

_{1,2}(u-u

_{0}, v).3. Perform inverse Fourier transform on the selected plot the Fourier spectrum with the transformation of a complex image with

_{1,2}(x, y).Then perform joint processing of complex images obtained from the 1st and 2nd images. This processing produces consistently for each point of the image, and it consists in the multiplication of 1 and a complex conjugate of the 2nd complex images

_{1}(x, y)(C

_{2}*(x, y), logarithmically received a new integrated image and allocate it the imaginary part. In Perna map values of the surface height of the original three-dimensional object relative to a flat surface.A narrow segment of the object image with sinusoidal bands can be described by the expression (1), in which vidnosti bands b(x, y) different from zero in a small limited area. For simplicity, consider a one-dimensional case. Let b(x)= rect(x/p), i.e. b(x)=1 for |x|p and b(x)=0 for |x|>p, where p is the width of the narrow section. It is known that the spectrum of such a rect-function equal to the function

B(u)=2psin(pu)/(pu), (7),

the width of the Central peak which 2/R. Suppose also that the function f

_{1}in the expression (6) is constant and small value, that is f

_{1}=<<1. This means that the object is selected in the form of narrow and low "steps". Then

where(.) - Delta-Dirac function. Substituting in (6) expression (7), (8) and using the filter property of the Delta function, we get

Whence it is seen that assmall value, the width of the spectrum in the +1st order is mainly determined by the width of the spectrum, which is equal to 2/R. In Fig.7 shows a graph of the module from this function in relative units.After image processing of the original three-dimensional nst throughout the image. As the strip outside of the object and the object obtained from different images, on the border of the object will be unpredictable shift of the bands, i.e. the phase shift. Shift by an integer number of bands are impossible to determine, therefore, the magnitude of this shift can not be more than 1/2 of the period of the stripes, which is equal to 1/u

_{0}. This means that the image can be described by the following equation (1), in which the phase of f

_{1}(x) =rect(x/p), where<1/2u

and vidnosti b=const. Then B(u) =(u) and

Estimate the width of the spectrum in the +1st order for the newly formed image with augmented bands. Substituting these expressions in (6), we obtain:

C

When comparing the obtained expression (10) with (9) shows that the spectrum of a new image (10) as for (9), mainly determined by the first term and it is much narrower than the range (9) of the original image. This fact is also confirmed by the results of numerical calculation of the spectrum in the +1st order from the new image, shown in Fig. 8. In the graph of Fig.7 spectrum width at the level of 0.1 to about isenia spectrum width in the1-x orders allows us to separate them from the zero order. Therefore, there is no overlap of the spectra and, consequently, improve the quality of the surface shape even on the narrow portions of the object.Thus, using the proposed method can measure the surface shape of any complex object with a simultaneous increase measurement accuracy.

Estimate the width of the spectrum in the +1st order for the newly formed image with augmented bands. Substituting these expressions in (6), we obtain:

C

_{1}(u) =(u)+j2psin(pu)/(pu). (10)When comparing the obtained expression (10) with (9) shows that the spectrum of a new image (10) as for (9), mainly determined by the first term and it is much narrower than the range (9) of the original image. This fact is also confirmed by the results of numerical calculation of the spectrum in the +1st order from the new image, shown in Fig. 8. In the graph of Fig.7 spectrum width at the level of 0.1 to about isenia spectrum width in the1-x orders allows us to separate them from the zero order. Therefore, there is no overlap of the spectra and, consequently, improve the quality of the surface shape even on the narrow portions of the object.Thus, using the proposed method can measure the surface shape of any complex object with a simultaneous increase measurement accuracy.

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