GB2199138A - An optical measuring system - Google Patents

Description

1 1- An Optical Measuring Syster2 199 138

FIELD OF THE INVENTION

The present invention relates to an optical measuring system.

BACKGROUND OF THE INVENTION

The results Obtained when using optical measuring systems of the prior art suffer inaccuracies due to errors introduced by reascn of aberrational and other optical effects in the optical components employed.

For example a known cptical system incorporates a laser device emitting a fine beam of light. The beam is directed onto a rotating mirror positioned at the focus of a lens such tht the omitted rays from the source scan the lens and are then brought into parallel by the lens to traverse an object to be measured, and then collected by a second lens which focuses the parallel beam onto a photocell or other similar device.

The object pas.sing through the beam will intercept a proportion of the laser light beam such that the photocell wi 11 output a-square wave signal having a centre dark portion proportional to the vertical dimensions of the object.

This system performs well within certain limitswhich are set by the inability of the lens system to perform to theoretlical requirements.

In order to-overcome zhe deficiences introducedinto the optical systems of the prior art because of

2 optical aberrations, a combination of lenses are employed to construct an optical lens system which, to a certain extent, is aberration free.

This art is complex as well as costly, and requires special skills to construct the necessary lens arrangement. SUMMARY OF THE INVENTION

It is an object of the present invention to obviate the difficulties of the prior art by providing a measuring system having the capability of compensating automatically for the errors introduced into the output measured result caused by the effects mentioned above.

According to the invention there is provided apparatus for measuring the dimensions of an object comprising lens means for projecting a beam of light across the is object from a point source of light placed at the focus of said lens means, said source emitting light rays at a scanning angle with respect to the principal axis of said lens means, means for determining the displacement of the respective extremities of said object and thus a dimension of the object, from said principal axis by monitoring said beam after interception by said object, and means derived from, ray tracing the light from said point source through said lens means for applying a correction factor to the measured value of each said determined displacement to compensate for inaccuracies due to optical aberration and distortion in said lens means.

1 1 t e 3 With the invention As claimed above, it is not necessary-that any mechanical skills be employed to construct an aberration f-ree system and indeed the invention may-be applied to any lens irrespective of shape or size.

BRIEF DESCRIPTION OF THE DRAWINGS

An embodiment of the present invention will now be described by way of example with reference to the accompanying drawings wherein:

Figure lis a schematic representation of an optical measuring system of the prior art; - Figure 2 illustrates the reasons which lead to inaccuracy of measurement of the prior art system shown in Figure 1;

Figure.3 illustrates the manner of evaluating the results obtained by the measuring system of the present inv ention corrected for optical aberration and distortion; Figures 4a, 4b and 4c illustrate ray tracing techniques for determining constants of the polynomial used to correct for aberrational.defectS in the lens of the measuring system of the invention; and Figure 5 is a table of results using a computer programme to determine the constants of the polynomial expression used to correct for aberrational effects of the lens system of the pr esent invention; and Fi gure 6 is a schematic diagram of electronic circuitry to correct for optical inaccuracy in an optical measuring 4 system utilising the technique of the invention.

BEST MODES OF CARRYING OUT THE INVENTION By way of explanation and background information, it is required in some production processes to perform dimensional measurements on static or moving objects and known prior art, see Figure 1 accompanying this disclosure, uses an optical system 1 which houses a laser 2 emitting a fine beam of light 3. This beam, is scanned by a rotating mirror 4 across the lens or lens system 5, so as to produce parallel beams 6 being scanned across an object 7 which is under test. The parallel beams are collected on lens 8 and subsequently focused on a photocell 9 which outputs a square wave signal 10 on which a centre dark portion 11 is proportional to the vertical dimension of object 7. This system performs well within certain limits these limits being set due to errors and aberrations in lens 5.

The effe,--ts of such errors and aberrations may be illustrated with reference to a simple lens 12 shown in Figure 2. If the lens 1.2 was an ideal lens, then beams emitted from the focal point 13 would produce parallel rays such as 14, 15 and so on. In practice, however, this is not the case as normal lenses have finite dimensions 16 and three possible sources of error occur.

Firstly, beams emitted from the focus would only produce parallel bundles such as 17 and 18 and not necessarily 1 1 1 r parallel beams throughout the aperture of the lens.

Secondly, due to the thickness of the lens, the beam emitted from the focus would be displaced through the angle 19 because of the refractive index of the lens material and the thickness of the actual lens.

Thirdly, in the application described herein,- in which a beam is scanned across the aperture of the lens, the angle of scan 17' is not proportional to the object dimension Y because of, not only the errors and aberrations previously-discussed, but also because of trigonometrical considerations.

Thus where g' is a small angle, the relationship between Y and O"Is approximately linear but as t increases this relationship becomes increasingly inaccurate.

It can be found by ray tracing through the system! that:

Y =A# e + Azo- 3. + A 3 19 5 A,,, 9L (-zm - 0) - For purposes of explanation a typical function for the variation in Y versus l- may be taken as Y = g- + R,... and the following table constructed 1 OC? showing the variation in Y against time t and 9' where 19is rotating at 1'/sec:

Time Y 1 1 0.99 2 1.92 3 2.73 4 3.36 In practice is rotating at a constant angular 2 3 ' 1 6 velocity and, therefore, t is directly proportional to P_ - lú we take an exatnpl( where an obi,et in thc nytttra obstructs the light beam, when t and 0- = 4, then the height of the object above the principal axis Y will be equal to 3.36.

Therefore it may be seen that with an object height of 3.36, a reading of 4 will be received and if this value is re-entered into the equation, then it will give the true value of Y and this is the principle on which the lens compensation system of the present invention works.

In practice, the coefficients used in each part of the power series depend on the focal length of the lens, the radius of the lens surface, the centre thickness of the lens and the distance of the object from the lens and are obtained by ray tracing techniques as mentioned above. These have to be calculated for each size of lens compensation system and the coefficients entered into the programme for that system. Normally, corrections only have to be applied up to the 3rd or, in extreme cases, the Sth order of the power series.

lore makes use of a polynomial The invention there expression to correct for optical system inaccuracy above referred to, given by Y = A#?- + A119 + A 9:" + A" where f is the scanning angle created by a rotating mirror 23 in a system whcih is scanning 7 r a laser beam across a lens of large dimension 22 with the mirror 23 at its focal point, see Figure 3, and Y is the object displacement from the principle axis.

This relationship as referred to above, is a result of mathematical calculations,-derived by ray tracing techniques, and can be-extended to the 7th and 9th orders, depending on the type of lens and the angle of sweep a - The ray tracing techniques involved and algebraic methods of determining the displacement of a ray through a lens and also the calculation of constants required to insert into the polynomical Y = A19 + A2.0 + AU4 A will be described herein. Such techniques and calculations are extremely complex and very lengthy and only a representative sample has been included in this disclosure.

A detailed-ray tracing technique will now be described with reference to Figure 4a, 4b and 4c.

It is to be observed that a centered optical system is one in which the centres of spherical surfaces and the axes of symmetry of aspherical surfaces, all lie on a single optical axis. A point lying on this ax,s is called an axial point, while one lying off-axis is called an extraaxial point. The plane containing an extraaxial point-and the lens axis is known as the meridian plane; it constitutes a plane of symmetry for the whole system. A ray lying in a meridian plane is called a 8 meridional ray.

For meridional rays, the origin of co-ordinates is placed at the vertex of a refracting or reflecting surface, with distances measured along the axis (X-axis) as positive to the right and negative to the left of this origin. Transverse distances in the meridional plane are considered positive if above the axis and negative below it.

The angle U to the axis of a meridional ray shall be regarded as positive if an anticlockwise rotation (or less than 90') takes us from the axis to the ray - this is contrary to Conrady's convention - and the angle of incidence I as positive if an anticlockwise rotation takes us from the normal to the ray.

Finally, all data relating to the portion of a ray lying in the space to the left of a surface (usually the object space) are represented by unprimed symbols, while data referring to the portion of a ray lying in the space to the right of the surface are denoted by primed symbols.

The path of a meridional ray through a single spherical refracting surface can be traced with high accuracy by the following (q,U) method.

Here the ray is defined in relation to the surface by stating the ray slope angle U and the perpendicular distance q of the ray from the surface vertex. To derive the ray tracing equations consider Figure 4a in which 1 9 a line has been drawn parallel to the ray through the centre_ of curvature of the surface. From the construction, r sin I r sin U + q, hence, sin I qc + sin V where c is the curvature of the surface, the reciprocal of the radius of curvature. Now by the law of refraction, -sin V = (nlln')sin I and sin.ce angle PCV is equal to I - U and V - U', evidently U' = U - 1 + V _Finally, the q' of the refracted ray is calculated by placing primes on all the terms in Eg. (1) giving qI = (sin V - sin U')/c This equation-is good when the radius of curvature is fairly short so that c is large, but at a weak surface of-lo.ing radius, I approaches U, so that qI becomes the ratio of two small numbers; while if the surface is plane, qI is actually 0/0 and is indeterminate. Consequently, other equations have been developed to replace this equation. In FigureMb), a perpendicular from the point of in--,id.--ii,ce P to the lens axis and another. perpendicular from the surface vertex V to the normal are drawn. OU = OP = g, say. Now a line is drawn parallel to the ray through 0 to divide q into two parts, the upper part being (g cos U) and the lower part (g cos I). Hence q = g/(cos U + cos I), and g = q/(cos U + cos I) The virtue of this expression is that cosines are always positive, and hence is always about equal to one half of q, more or less. Under no circumstances can this expression become indeterminate. By adding primes everywhere, the final expression is reached: q = g(cos U' + cos V) The transfer of the ray from one surface to next is clear from Figure4(c) in which q = g' + t sin U' (Clearly U = U') The meridional ray tracing equations may be summarized as follows:

sin I qc + sin U sin V (n/n')sin I U, = U - I + I, Short radius only:

q' = (sin V - sin U')/c Universal:

g = q/(cos U + cos I) q'= g(cos U' + cos I') opening 11 Initial q = -d sin U Transfer:

q = qI + t sin U' Closing: - d' = -(final q')/(final sin U') It is now possibl e to derive the third order approximation from the ray tracing equations.

- Supposethat the U and q of a meridional ray at a spherical surface can be calculated approximately from the following cubics in an arbitrary variable S: sin U A$ S + A 3 S q = B S + B,, S -3 the equality_symbol being used in this context to relate two approximately equal quantities. Sin U rather than U is defined because the algebraic manipulations areslightly easier.

Then using the ray tracing equations and power series for trigonometric and inverse trigonometric functions. U = A, S + (l/6A3 + A.5)S3 3 3 sin I-= (BIS + B3S)C + (AlS + A 3 S) 3 E# S + Ej S where E,= A$4-B# c andE,=A 3 + Bc It follows that sin I'= E3 S3 Now I = sin I + 1/6sin3 I and V = K sin I + 1/6k 3 sin 3, -25 where k = n/n', hence U' = U + (kl) sin I + 1/6(K 3 _ 1) sin 3, = A S + (l/6A3 + A)S3 + (k - 1) (E j S + E 3 S 3) + 1/6(k 3 -,1) E 3S3 1.

(k E - B c)s + (l/6((k 3 1) E' + A' + k E3 - B c)S, sin U' = U' -1/W C3 sin U' = 1/6(K 3 - 1) E 3 + A 3 _ (k E# - B, c + k E3 - B3 c -A 3 -3K E B c (k E9 - B& c) + B 3C3) + k E3 - B. c = -1/6 (E 3 = -1/6(3A,B,c (A, + Ble) - 3K E,Bc (k E - B t cH + k E3 - B 3 c k E 3 - (l/2E B 1 (A, - k (k E # - B, c) + B3) c Therefore sin U' A'S + A'S where A' = k E, B, c and A' k E - (F + B,3)c where F 1/2E1BI(A1 - k (k E, - B c = 1/2E1BI(A1 - k A',) Then q 1 = (k E j -A',)/c S + (k E 3 - A) /c S = B', S + B S where BS = B and B = E + B 3 In practice, the above equations are used to calculate series of constants which have been included into computer programme which itself has produced numerical values for the coefficients A,, A2_p A_, A,, thus enabling the complete correction and calculation of displacement Y to be effected.

As shown above, bv accepting this polynomical expression, the coefficients A,, A,., A_Z.... A,, may be derived 21 X J1 1 4 13 and an accurateresult provided of the dimension Y in relation to the scanning angle P. By evaluating Y for both extremes of the object to be measured for example, object 7 in Figure 3, the object dimension is found as an algebraic difference of Y, and Y. see Figure 3. The significance of this method is such that, when applied in practical cases,.it means that an accurate measurement of an object may be made irrespective of the position of the object within the measuring field of the lens.

In order to calculate the contants A,, A2_, A.3 A....a special progra"e has been developed and a table of results using- the programme is given, see Figure 5, as an example tor one particular instance, where CF1Y is the coefficient A, CF2Y is the coefficient A and CF3Y is the coefficient A Column 1: Column 2:

Column 3:

Column 4:

Lists angle U starting from 0-7.5' S angle-between ideal ray trace and k actual trace Y this is object height in mm The resultant scanned angle without compensation.

Here, large discrepancies can be seen between values in Column.4 and in Column 3, and when we apply compensation in the 3rd order, Column 5, the results can be closer to that in Column 3. When we finally apply compensation of the 5th order is applied, results are almost identical to the theoretical values in Column 3.

k 14 Typical apparatus for obtaining the results to be corrected by the technique of the invention, is of the type shown in Figure 1.

The output from the photocell 9 is fed to specially designed electronic circuitry shown schematically and operationally labelled in Figure 6, which processes the output and performs calculations to the degree desired in the expression Y = f (9-) defined above to correct for system accuracy.

A 1

Claims (4)

1. CLAIMS Apparatus for measuring the dimensions of an object comprising lens

   means for projecting a beam of light across the object from a point source of light placed at the focus of said lens means, said source emitting light rays at a scanning angle with respect to the principal axis of said lens means, means for determining the displacement of the respective extremities of said object from said principal axis by monitoring said_ beam after interception by said object, and means for applying a correction factor derived from ray tracing the light from said point source through said lens means to the measured.value of each said determined displacement to compensate for inaccuracies due to optical aberration and distortion in said lens means.
2. 2. Apparatus as claimed in claim 1 wherein said correction factor applying means includes computer means for calculating said correction factor from the expression Y =- A% 0 + A7_9. + A3 9 A h J where:

   Y is a said measured value of the object; A, A., A,, are constants dependent on the focal length of the lens- means, radius of the surface of the lens means, centre thickness of the lens means and the object distance from the lens means; and tL 16 g- is the scanning angle with respect to the optical axis of said lens means made by that ray of light from said source which delimits a said measured value in said parallel beam after deviation in said lens means.
3. 3. Apparatus as claimed in claim 1 or 2 further including calculating means for forming the algebraic difference of a corrected said measured value of one extremity and a corrected said measured value of the other extremity of the object with respect to said optical axis, whereby to provide the dimension of the object between said two extremities.
4. 4. Apparatus for measuring the dimensions of an object substantially as hereinbefore described with reference to the drawings.

   Publisiic! 1988 a, The Patent Office. Statz House. 66 71 '-- C--. Hol,n r. !--- I)rI WClR 4TF Further Oopes may be obLamed from The Patent office. Sales Branch, St Mary Cray, Orpung'4oi- Kent BR5 3-RD Pi,inx.1 b,, Multiplex techniqaes IW, SL Mary Cray. Kent. Con. 1/87