CN111649696B - High-precision calibration method for structured light measurement system - Google Patents
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/25—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures by projecting a pattern, e.g. one or more lines, moiré fringes on the object
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Abstract
The invention discloses a high-precision calibration method of a structured light measurement system, which comprises the steps of sending projection light to the surface of an object to be measured through a projection device, projecting the projection light onto the object to be measured through grating stripes, and carrying out linear brightness balance on the projection light before the projection device sends out transmitted light through a linear brightness balance method; the image acquisition device acquires projection light on the surface of an object to be measured to form a projection light image, and when the projection light image is formed, sinusoidal stripes generated by the projection light are compensated to form ideal sinusoidal stripes; the projection light image is demodulated to obtain the three-dimensional information of the measured object, the fitting plane replaces the original substrate phase, the high-precision imaging is realized, the problems of poor uniformity of projection stripes, primary noise of the stripes and uneven substrate phase generated in the projection process are periodically solved, and the method effectively improves the structural light detection precision.
Description
Technical Field
The invention relates to the field of structured light three-dimensional measurement, in particular to a high-precision calibration method for a structured light measurement system.
Background
In the three-dimensional measurement of an object, a structured light measurement technology is a commonly used three-dimensional measurement method of the object, the structured light measurement technology is a technology for realizing the three-dimensional measurement through active and non-contact optical measurement, structured light is projected and projected on the measured object through grating stripes which form a certain angle direction with projected light on the basis of optical triangulation measurement, light information on the projected object is structurally coded, and the corresponding three-dimensional information of the measured object is obtained through computer decoding and corresponding algorithms.
In the industry, there are more structured light products, which have three forms, the first is the manufacturer of 3D sensor based on structured light, mainly producing small structured light sensors for the application of automation equipment companies; the second is a company dedicated to 3D measurements, the structural light module is only one of the core modules; the third type is mainly used for measuring large workpieces, mainly focuses on measuring large workpieces, and the existing popular structured light measuring method has the following problems:
1. the projector is arranged at a certain angle, and the projected fringe brightness and the fringe intervals are inconsistent, so that a phase-resolving error exists in the phase-resolving process, and errors are brought to a subsequent measurement structure;
2. the fringe period does not completely correspond to the phase shift fringe period, the boundary of the period is aligned, and the fringe has noise;
3. due to the material problem of the substrate of the actual projection, problems of phase tilt, extra noise introduction, measurement accuracy loss and the like can occur.
Disclosure of Invention
The invention aims to provide a high-precision calibration method for a structured light measurement system, which aims to solve the problems in the prior art.
In order to achieve the above purpose, the invention provides the following technical method:
a high-precision calibration method for a structured light measurement system comprises the following steps:
step S1: the projection device emits projection light to the surface of an object to be measured, linear brightness balance is carried out on the projection light before the projection light is emitted, the projection light is projected onto the object to be measured through grating stripes, and the grating stripes and the projection light form a certain angle;
step S2: the image acquisition device acquires projection light on the surface of an object to be measured to form a projection light image, and performs fringe sine compensation on the projection light image to obtain ideal projection fringes;
step S3: and demodulating the projection light image to obtain phase information, and acquiring the three-dimensional information phase of the measured object according to the phase information and a fitting plane generated by the structured light measurement system so as to acquire the three-dimensional information of the measured object.
Preferably, before the projection device emits the projection light in step S1, grating stripes are generated, and the generated grating image is subjected to linear brightness balance, where the linear brightness balance method includes the following steps:
step S11, the projection device emits projection light to the surface of the measured object, before the projection light is emitted, the projection device calculates the grating stripe of the projection light to obtain regular periodic sine stripe and generate a grating image;
and step S12, performing digital linear processing on the grating image, performing brightness balance to obtain uniform sine stripes, and performing brightness balance on the grating image because the projection light and the projected object form a certain angle to cause the brightness of the stripes in the whole field range to have a linear descending trend.
Further, the step S11 generates irregular periodic sinusoidal stripes according to the formula:
I(x，y)＝A+Bcos(2πfu+δ)；
wherein, I (x, y) is the distribution of the light intensity in the x and y directions for generating the irregular periodic sine stripes, A + B is the brightness value of the grating image, f is the frequency of the uniform sine stripes, u is the ratio of the projection period to the resolution,
delta is the phase shift;
the value of the resolution of the projector is height × width, height is the number of pixels in length, width is the number of pixels in width, and x is the distribution of the light intensity of the irregular periodic sine stripes in the x direction.
The distribution of the irregular periodic sine stripes is related to the distribution of projection light intensity and brightness value, the light intensity is in direct proportion to the brightness value, the high brightness value causes the sine stripes to move upwards integrally or the upper half part is larger than the lower half part, and the low brightness value causes the sine stripes to move downwards integrally or the lower half part is larger than the upper half part.
Further, in step S12, the grating image is digitally and linearly processed to obtain the uniformity sine stripe according to the formula:
I(x，y)＝A+Bcos(2πfu+δ)g(1-ku)；
wherein k is a transform coefficient, and I (x, y) makes the brightness value of the raster image change linearly within the range of [0, A + B ].
Preferably, in step S2, the image capturing device captures projection light on the surface of the measured object, and when forming the projection light image, the image capturing device performs fringe period compensation on fringes generated by the projection light, so as to compensate the projection image projected by the structured light, and form an ideal image, and the fringe period compensation method includes the following steps:
step S21, the measured object emits transmission light through the projection device in the vertical direction, and sine stripes are generated on the projection working surface, so as to realize theoretical imaging;
step S22, the projection device and the projection working surface form a certain angle, the sine stripe generated by the actual imaging of the transmission light on the projection working surface has deformation, and the deformation sine stripe is reversely transformed at the projection position;
and step S23, respectively calculating the proportion of the sine stripes which are reversely transformed in 2 half periods, modifying the sine stripes according to the proportion, and normalizing the range of the sine stripes of 2 half periods to the interval of [0,1] to obtain the normal sine stripes in one period.
Further in step S21, according to the formula:
θ＝arctan(AB/2f)；
the measured object is AB, O is the optical center of the projection device, theta is the half angle corresponding to the grating, and f is the focal length of the lens.
Further, in step S23, the proportion of the sine stripe converted in the opposite direction in the half period is calculated according to the formula:
wherein the content of the first and second substances,
the half-period proportion of O ' B ' to the theoretical imaging of the vertical projection is adopted, under the condition of the vertical projection of the projection lens, the theoretical imaging of the projection working surface is A ' B ', wherein the vertical intersection point of B ' and the projection working surface is H ', O ' is an imaging point of the optical center of the projection lens corresponding to the projection working surface, A ' B ' is the actual imaging of the projected object on the projection working surface, and alpha is the projection angle;
and performing half-cycle correction compensation on the deformed sine stripes through the formula.
Further, in step S23, the normal sine stripe in one period consists of two half-period sine stripes according to the formula:
wherein, delta theta is a half angle corresponding to the projected object in one period;
and (3) changing and adjusting the sine stripes in one period according to the proportion, carrying out phase transformation on the maximum value in the period, and normalizing the maximum value in the period to the range of the interval [0,1] to obtain the normal sine stripes in a single period.
Preferably, in step S3, the calibrating step of the measurement system in advance according to the phase information of the measured object to obtain the three-dimensional information of the measured object, and the obtaining step of the three-dimensional information of the measured object by using the fitting plane instead of the original substrate phase includes the following steps:
step S31, performing phase solution on the object with the sine stripes, namely subtracting the original substrate phase, wherein the original substrate phase is a matrix stored locally;
step S32, fitting a plane according to a least square method;
step S33, the base phase plane is replaced with the fitted plane.
Further, the step S32 includes:
according to the formula:
wherein x, y and z are three-dimensional space points corresponding to a fitting plane respectively, a, b and c are coefficients, and the task of the fitting plane is to solve the coefficients a, b and c;
wherein epsiloniAs residual values of the fitted plane, (x)i,yi,zi) N three-dimensional space points;
according to the principle of least square method, when the formula is established, a, b and c are coefficients of plane fitting, S is a fitting plane, and the fitting plane is used for replacing the original substrate phase plane.
Compared with the prior art, the invention has the beneficial effects that:
1. the linear brightness balance method compensates the brightness and the fringe intervals of the projection fringes to generate uniform sine fringes, so that the influence caused by poor uniformity is compensated, and the measurement error is reduced;
2. the sine stripes are periodically compensated and corrected, so that the influence of factors such as projection defocusing and the like is reduced, normal sine stripes are obtained through compensation, and the structured light detection precision is effectively improved;
3. and the fitting plane is used for replacing the original substrate phase, so that the measurement precision is simply and effectively improved.
Drawings
In order that the present invention may be more readily and clearly understood, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments that are illustrated in the appended drawings.
FIG. 1 is a flow chart of a method for calibrating a structured light measurement system with high accuracy according to the present invention;
FIG. 2 is a schematic structural diagram of a high-precision calibration method for a structured light measurement system according to the present invention;
FIG. 3 is a schematic diagram of a projection structure of a high-precision calibration method for a structured light measurement system according to the present invention;
FIG. 4 is a schematic diagram of an actual projection curve and a theoretical curve of a high-precision calibration method for a structured light measurement system according to the present invention;
FIG. 5 is a schematic diagram of fringe variation for compensating sinusoidal fringes according to the high-precision calibration method for a structured light measurement system of the present invention.
Detailed Description
The technical method in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-2, in an embodiment of the present invention, a method for calibrating a structured light measurement system with high precision includes the following steps:
step S1: the projection device emits projection light to the surface of an object to be measured, linear brightness balance is carried out on the projection light before the projection light is emitted, the projection light is projected onto the object to be measured through grating stripes, and the grating stripes and the projection light form a certain angle;
step S2: the image acquisition device acquires projection light on the surface of an object to be measured to form a projection light image, and performs fringe sine compensation on the projection light image to obtain ideal projection fringes;
step S3: and demodulating the projection light image to obtain phase information, and acquiring the three-dimensional information phase of the measured object according to the phase information and a fitting plane generated by the structured light measurement system so as to acquire the three-dimensional information of the measured object.
In step S1, before the projection device emits the projection light, generating a grating pattern, and performing linear brightness balance on the generated grating image, the linear brightness balance method includes the following steps:
step S11, the projection device emits projection light to the surface of the measured object, before the projection light is emitted, the projection device calculates the grating stripe of the projection light to obtain regular periodic sine stripe and generate a grating image;
in step S12, since the projection light and the projected object form a certain angle, the brightness of the stripes in the whole field of view decreases linearly, and the grating image is processed digitally and linearly to balance the brightness, so as to obtain uniform sinusoidal stripes.
In step S11, irregular periodic sinusoidal stripes are generated according to the formula:
I(x，y)＝A+Bcos(2πfu+δ)；
wherein, I (x, y) is the distribution of the light intensity in the x and y directions for generating the irregular periodic sine stripes, A + B is the brightness value of the grating image, f is the frequency of the uniform sine stripes, u is the ratio of the projection period to the resolution,
delta is the phase shift;
the value of the resolution of the projector is height × width, height is the number of pixels in length, width is the number of pixels in width, and x is the distribution of the light intensity of the irregular periodic sine stripes in the x direction.
The distribution of the irregular periodic sine stripes is related to the distribution of projection light intensity and brightness value, the light intensity is in direct proportion to the brightness value, the high brightness value causes the sine stripes to move upwards integrally or the upper half part is larger than the lower half part, and the low brightness value causes the sine stripes to move downwards integrally or the lower half part is larger than the upper half part.
In step S12, the grating image is digitally and linearly processed to obtain a uniform sinusoidal fringe according to the formula:
I(x，y)＝A+Bcos(2πfu+δ)g(1-ku)；
wherein k is a transform coefficient, and I (x, y) makes the brightness value of the raster image change linearly within the range of [0, A + B ].
In step S2, the image capturing device captures projection light on the surface of the measured object, and when a projection light image is formed, performs fringe period compensation on fringes generated by the projection light, so as to compensate projection imaging of structured light projection, and form an ideal imaging, where the fringe period compensation method includes the following steps:
step S21, the measured object emits transmission light through the projection device in the vertical direction, and sine stripes are generated on the projection working surface, so as to realize theoretical imaging;
step S22, the projection device and the projection working surface form a certain angle, the sine stripe generated by the actual imaging of the transmission light on the projection working surface has deformation, and the deformation sine stripe is reversely transformed at the projection position;
and step S23, respectively calculating the proportion of the sine stripes which are reversely transformed in 2 half periods, modifying the sine stripes according to the proportion, and normalizing the range of the sine stripes of 2 half periods to the interval of [0,1] to obtain the normal sine stripes in one period.
In step S21, according to the formula:
θ＝arctan(AB/2f)；
the measured object is AB, O is the optical center of the projection device, theta is the half angle corresponding to the grating, and f is the focal length of the lens.
In step S23, the ratio of sine stripes of the inverse transformation within a half period is calculated according to the formula:
wherein the content of the first and second substances,
the half-period proportion of O ' B ' to the theoretical imaging of the vertical projection is adopted, under the condition of the vertical projection of the projection lens, the theoretical imaging of the projection working surface is A ' B ', wherein the vertical intersection point of B ' and the projection working surface is H ', O ' is an imaging point of the optical center of the projection lens corresponding to the projection working surface, A ' B ' is the actual imaging of the projected object on the projection working surface, and alpha is the projection angle;
and performing half-cycle correction compensation on the deformed sine stripes through the formula.
In step S23, the normal sinusoidal stripe in one period consists of two half-period sinusoidal stripes according to the formula:
wherein, delta theta is a half angle corresponding to the projected object in one period;
and (3) changing and adjusting the sine stripes in one period according to the proportion, carrying out phase transformation on the maximum value in the period, and normalizing the maximum value in the period to the range of the interval [0,1] to obtain the normal sine stripes in a single period.
In step S3, the measurement system calibrates the measurement system in advance according to the phase information of the measured object to obtain the three-dimensional information of the measured object, and the obtaining of the three-dimensional information of the measured object and the replacing of the original substrate phase by the fitting plane includes the following steps:
step S31, performing phase solution on the object with the sine stripes, namely subtracting the original substrate phase, wherein the original substrate phase is a matrix stored locally;
step S32, fitting a plane according to a least square method;
step S33, the base phase plane is replaced with the fitted plane.
Step S32 includes:
according to the formula:
wherein x, y and z are three-dimensional space points corresponding to a fitting plane respectively, a, b and c are coefficients, and the task of the fitting plane is to solve the coefficients a, b and c;
wherein epsiloniAs residual values of the fitted plane, (x)i,yi,zi) N three-dimensional space points;
according to the principle of least square method, when the formula is established, a, b and c are coefficients of plane fitting, S is a fitting plane, and the fitting plane is used for replacing the original substrate phase plane.
Examples
Referring to fig. 3-5, in the embodiment of the invention, the linear luminance balancing method generates irregular periodic sinusoidal stripes according to the formula:
I(x，y)＝A+Bcos(2πfu+δ)＝255cos(2π*1*0.2+0.3)＝255*0.02＝5.1；
wherein, I (x, y) is the distribution value of the light intensity in the x and y directions for generating the irregular periodic sine stripes of 5.1, a + B is the brightness value of the raster image of 255, f is 1 is the frequency of the uniform sine stripes, u is the ratio of the projection period to the resolution,
δ is 0.3 phase shift;
wherein the resolution value is 800 x 600,
the sine of the irregular periodic sine stripes is related to the distribution of projection light intensity and brightness value, the light intensity is in direct proportion to the brightness value, the high brightness value causes the sine stripes to move upwards integrally or the upper half part is larger than the lower half part, the low brightness value causes the sine stripes to move downwards integrally or the lower half part is larger than the upper half part, the grating image is subjected to linear processing to obtain uniform sine stripes, and according to a formula:
I(x，y)＝A+BcoS(2πfu+δ)g(1-ku)＝5.1*g(1-1*0.2)＝4.08；
where k is 1, which is a transform coefficient, and I (x, y) linearly changes the raster image luminance value in the range of [0, 255 ].
And performing fringe period compensation on the generated sine fringes, wherein the measured object is AB-9.8, and O is the optical center of the projection device, and according to the formula:
θ＝arctan(AB/2f)＝arctan(9.8/2*20.24)＝13.6°；
where θ is the half angle corresponding to the object to be projected, and f is 20.24, the frequency of the uniform sinusoidal stripes is the frequency of the generated uniform sinusoidal stripes.
Calculating the proportion of sine stripes of the reverse transformation in the half period according to the formula:
wherein the content of the first and second substances,
the half-period proportion of O ' B ' to the theoretical imaging of the vertical projection is adopted, in the case of the vertical projection of the projection lens, the theoretical imaging of the projection working surface is A ' B ', wherein the vertical intersection point of B ' and the projection working surface is H ', O ' is an imaging point of the optical center of the projection lens corresponding to the projection working surface, A ' B ' is the actual imaging of the object to be projected on the projection working surface, and alpha is 45 degrees and is the angle of the projection;
and performing half-cycle modification compensation on the deformed sine stripes through the formula.
The normal sinusoidal stripe in one period consists of sinusoidal stripes of two half periods according to the formula:
wherein, Delta theta is a half angle corresponding to the projected object in a single period;
and (3) changing and adjusting the sine stripes in one period according to the proportion, carrying out phase transformation on the maximum value in the period, and normalizing the maximum value in the period to the range of the interval [0,1] to obtain the normal sine stripes in a single period.
Fitting a plane to replace the original substrate phase method according to the formula:
wherein x, y and z are three-dimensional space points corresponding to a fitting plane respectively, a, b and c are coefficients, and the task of the fitting plane is to solve the coefficients a, b and c;
wherein epsiloniAs residual values of the fitted plane, (x)i,yi,zi) N three-dimensional space points;
according to the principle of least square method, when the formula is established, a, b and c are coefficients of plane fitting, S is a fitting plane, and the fitting plane is used for replacing the original substrate phase plane.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Claims (10)
1. A high-precision calibration method for a structured light measurement system is characterized by comprising the following steps:
step S1: the projection device emits projection light to the surface of an object to be measured, linear brightness balance is carried out on a grating image generated by the projection light before the projection light is emitted, the projection light is projected onto the object to be measured through grating stripes, and the grating stripes and the projection light form a certain angle;
step S2: the image acquisition device acquires projection light on the surface of an object to be measured to form a projection light image, and performs fringe sine compensation on the projection light image to obtain ideal projection fringes;
step S3: and demodulating the projection light image to obtain phase information, and acquiring the three-dimensional information phase of the measured object according to the phase information and a fitting plane generated by the structured light measurement system so as to acquire the three-dimensional information of the measured object.
2. The method for calibrating a structured light measuring system with high precision as claimed in claim 1, wherein in step S1, before the projection device emits the projection light, grating stripes are generated to perform linear brightness balance on the generated grating image, and the method for performing linear brightness balance comprises the following steps:
step S11, the projection device emits projection light to the surface of the measured object, before the projection light is emitted, the projection device calculates the grating stripe of the projection light to obtain regular periodic sine stripe and generate a grating image;
and step S12, performing digital linear processing on the grating image, and performing brightness balance to obtain uniform sine stripes.
3. The method for calibrating a structured light measurement system with high precision as claimed in claim 2, wherein the step S11 is to generate irregular periodic sinusoidal stripes according to the formula:
I(x，y)＝A+Bcos(2πfu+δ)；
wherein I (x, y) isThe distribution of the light intensity of the irregular periodic sine stripes in the x and y directions, A + B is the brightness value of the grating image, f is the frequency of the uniform sine stripes, u is the ratio of the projection period to the resolution,
delta is the phase shift;
the value of the resolution of the projector is height × width, height is the number of pixels in length, width is the number of pixels in width, and x is the distribution of the light intensity of the irregular periodic sine stripes in the x direction.
4. The method for calibrating a structured light measurement system with high precision as claimed in claim 3, wherein in step S12, the grating image is digitally and linearly processed to obtain the uniform sine stripes according to the formula:
I(x，y)＝A+Bcos(2πfu+δ)g(1-ku)；
wherein k is a transform coefficient, and I (x, y) makes the brightness value of the raster image change linearly within the range of [0, A + B ].
5. The method for calibrating a structured light measurement system with high accuracy as claimed in claim 1, wherein in step S2, the image capturing device captures the projected light from the surface of the measured object, and when forming the projected light image, the fringe period compensation is performed on the fringes generated by the projected light for compensating the projected image of the structured light projection to form the ideal image, and the fringe period compensation method comprises the following steps:
step S21, the measured object emits transmission light through the projection device in the vertical direction, and sine stripes are generated on the projection working surface, so as to realize theoretical imaging;
step S22, the projection device and the projection working surface form a certain angle, the sine stripe generated by the actual imaging of the transmission light on the projection working surface has deformation, and the deformation sine stripe is reversely transformed at the projection position;
and step S23, respectively calculating the proportion of the sine stripes which are reversely transformed in 2 half periods, modifying the sine stripes according to the proportion, and normalizing the range of the sine stripes of 2 half periods to the interval of [0,1] to obtain the normal sine stripes in one period.
6. The method for calibrating a structured light measurement system with high precision as claimed in claim 5, wherein in step S21, according to the formula:
θ＝arctan(AB/2f)；
the measured object is AB, O is the optical center of the projection device, theta is the half angle corresponding to the grating, and f is the focal length of the lens.
7. The method for calibrating a structured light measurement system with high precision as claimed in claim 6, wherein the step S23 is to calculate the proportion of sine stripes inverted in one half period according to the formula:
wherein the content of the first and second substances,
the half-period proportion of O ' B ' to the theoretical imaging of the vertical projection is adopted, under the condition of the vertical projection of the projection lens, the theoretical imaging of the projection working surface is A ' B ', wherein the vertical intersection point of B ' and the projection working surface is H ', O ' is an imaging point of the optical center of the projection lens corresponding to the projection working surface, A ' B ' is the actual imaging of the projected object on the projection working surface, and alpha is the projection angle;
and performing half-cycle correction compensation on the deformed sine stripes through the formula.
8. The method for calibrating a structured light measurement system with high accuracy as claimed in claim 7, wherein in step S23, the normal sine stripe in one period consists of two half periods of sine stripes according to the formula:
wherein, delta theta is a half angle corresponding to the projected object in one period;
and (3) changing and adjusting the sine stripes in one period according to the proportion, carrying out phase transformation on the maximum value in the period, and normalizing the maximum value in the period to the range of the interval [0,1] to obtain the normal sine stripes in a single period.
9. The method for calibrating a structured light measurement system with high precision as claimed in claim 1, wherein the step S3 is that the measurement system is calibrated in advance according to the phase information of the measured object to obtain the three-dimensional information of the measured object, and the step of obtaining the three-dimensional information of the measured object and replacing the original substrate phase with the fitting plane comprises the following steps:
step S31, performing phase solution on the object with the sine stripes, namely subtracting the original substrate phase, wherein the original substrate phase is a matrix stored locally;
step S32, fitting a plane according to a least square method;
step S33, the base phase plane is replaced with the fitted plane.
10. The method for calibrating a structured light measurement system with high precision as claimed in claim 9, wherein the step S32 comprises:
according to the formula:
wherein x, y and z are three-dimensional space points corresponding to a fitting plane respectively, a, b and c are coefficients, and the task of the fitting plane is to solve the coefficients a, b and c;
wherein epsiloniAs residual values of the fitted plane, (x)i，yi，zi) N three-dimensional space points;
according to the principle of least square method, when the formula is established, a, b and c are coefficients of plane fitting, S is a fitting plane, and the fitting plane is used for replacing the original substrate phase plane.
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