DE102014207058A1 - Method for measuring and reconstructing curved, reflecting surfaces - Google Patents

Abstract

The present invention relates to a method with which curved, reflecting surfaces can be measured and reconstructed. The surfaces are optically measured and their structure is reconstructed by means of mathematical algorithms. According to the invention, in the method the curved, reflecting surface is illuminated with collimated beams, the light reflected from this surface is detected, and its structure is reconstructed therefrom by means of mathematical algorithms. In particular, the curved, reflecting surface is illuminated with collimated beams from different, defined directions and / or at different, defined angles of incidence and the reflected light is detected telecentrically. The reconstruction of the curved, reflecting surface is carried out by means of a geometric model and a system of differential equations. Although the proposed method is intended in particular for biometrics in the clinical diagnosis of ophthalmology, it can also be used for measuring and reconstructing curved, specular surfaces in other technical fields, such as industrial quality control.

Description

The present invention relates to a method with which curved, reflecting surfaces can be measured and reconstructed. The curved, reflecting surfaces are optically measured and their structure is reconstructed by means of mathematical algorithms.

Measuring a specular surface and then reconstructing its uniformly curved structure is well known for a variety of applications. According to the known state of the art, in particular two variants have developed, which will be briefly discussed below.

The first variant is based on the measurement of the distance between the light source or sensor and the respective impact location on the uniformly curved structure. Here, optical measurement methods are used, with which the 3D structure of the surface along a line or curve or over a 2D field is scanned with the aid of a measuring beam. The optical measuring methods used for this purpose can be based, for example, on optical coherence tomography (OCT), time of flight (TOF), laser triangulation (LT), or the like. On the basis of the spatial pattern resulting from the distance measurement, mathematical means such as spatial interpolation, least squares method o. A. reconstructed a geometric model of the uniformly curved structure.

Measurement and evaluation of this first variant are, for example, of T. Hellmuth and others in [1] and T. Swartz and others described in [2]. In the OCT method, coherent light is used with the aid of an interferometer for distance measurement on reflective and scattering samples. In the human eye, OCT techniques deliver measurable signals when scanning in depth, due to refractive index changes occurring at optical interfaces and due to volume scattering.

This example in US 5,321,501 described basic principle of the OCT method is based on white light interferometry and compares the duration of a signal using an interferometer (usually Michelson interferometer). The arm with known optical path length (= reference arm) is used as a reference to the measuring arm in which the sample is located. The interference of the signals from both arms gives a pattern from which one can determine the scattering amplitudes as a function of the optical delays between the arms and thus a depth-dependent scattering profile, which is referred to as A-Scan in analogy to the ultrasound technique. In the multidimensional scanning methods, the beam is then guided transversely in one or two directions, enabling a planar B-scan or a three-dimensional volume tomogram to be recorded. The amplitude values of the individual A-scans are displayed in linear or logarithmized greyscale or false color values. The technique of capturing single A-scans is also referred to as Optical Coherence Domain Reflectometry (OCDR), whereas OCT realizes two- or three-dimensional imaging by lateral scanning.

In contrast, in the second variant, also referred to as deflectometry, a designed 2D pattern is projected onto the uniformly curved surface. The surface-reflected virtual image of the designed 2D pattern is captured by a camera system. By analyzing the distortions caused by discrete areas of the curved surface, the surface can be reconstructed as a geometric model. Again, mathematical algorithms are used for the reconstructed structure. Most importantly, the virtual image of the designed 2D pattern is registered using an image processing technique. For this, it is sufficient to register individual pairs of irradiation and reflection vectors based on the available parameters from the system design. Only then is a reconstruction of the surface possible.

A typical example of this variant is the use of so-called Placido disks, which has a concentric alternating black and white rings existing ring system. This ring system is projected onto the anterior surface of the cornea, the ring-shaped reflex images are taken with a camera and usually evaluated computer-aided. Depending on the curvature of the cornea, the reflected ring pattern detected by the camera is distorted. In order to obtain a determination of the curvature from these reflection signals, the distortions of the rings must be compared with a known shape, which is usually chosen as a sphere with a radius of 7.8 mm. Such a solution is for example in the Scriptures US 4,685,140 A described.

The Placido disks used to produce concentric rings do not necessarily have to be flat. Such plane Placido disks are indeed sufficient in the prior art known and for example in US 5,110,200 A and US 5,194,882 A However, more widespread are funnel-shaped ( US 5,684,562 A . US 6,116,738 A ) or even spherically curved ( US 5,864,383 A ) Placido slices.

That in the DE 198 57 001 A1 described combination device is also suitable for non-contact determination of the corneal curvature of the eye. In this solution, six symmetrically arranged, collimated light beams are projected onto the eye and the light reflected from the cornea is detected telecentrically. The illumination is preferably carried out by means of IR light so as not to hinder the fixation of the patient's eye on a fixation light. A telecentric aperture and corresponding collimators ensure that the angles of incidence for the measurements are constant and independent of the axial position of the patient's eye. The evaluation is based on an ellipse model, which contains two perpendicular radii and an orientation angle. The surface of the cornea is reconstructed on the basis of the measured distances and the toric model.

In general, such methods often have problems in aligning the system, as well as achieving and maintaining the focus state. In addition, since reflection signals from the environment have a very disturbing effect, this must be taken into account when constructing and / or installing the device.

Although the above-described two variants for measuring and reconstructing the specular surface of a uniformly curved structure have been widely used in recent decades, the methods still suffer from disadvantages which adversely affect their accuracy, robustness and flexibility.

• • Probleme bei der Synchronisation zwischen Messgerät und Oberfläche während der Messung;
• • Probleme bei der Fokussierung des Imaging-Systems auf kleine Oberflächen, insbesondere bei einem geringem Abstand zur Oberfläche;
• • Auswirkung auch kleiner Verschiebungen der Oberfläche zur Bildachse auf die aufgezeichneten virtuellen Bilder, insbesondere bei einer vergrößerten Darstellung;
• • Auswirkung auch kleiner Neigungen asphärischer und konvexer Oberflächen auf die aufgezeichneten virtuellen Bilder, insbesondere bei einer vergrößerten Darstellung;
• • Überlagerung der in den aufgezeichneten Daten enthalten virtuellen Bild der gemessenen Oberfläche durch Umgebungsbeleuchtung und diffuse Reflexionen an lichtundurchlässigen Schichten.

When scanning non-stationary surfaces, such as the human cornea, in addition to the following difficulties can be expected, the list is not exhaustive:

• • Problems with the synchronization between meter and surface during the measurement;
• • problems in focusing the imaging system on small surfaces, especially at a small distance from the surface;
• • the effect of small shifts of the surface to the image axis on the recorded virtual images, especially in an enlarged representation;
• The effect of even small inclinations of aspheric and convex surfaces on the recorded virtual images, especially in an enlarged representation;
• • Superposition of the virtual image of the measured surface contained in the recorded data by ambient lighting and diffuse reflections on opaque layers.

Literature:

• [1] T. Hellmuth, J. Wei, Optical Coherence Tomography Corneal Mapping Apparatus US patent 5491524 A , filed in 1994, published in Feb. 1996.
• [2] T. Swartz, L. Marten and M. Wang, Measuring the cornea: the latest developments in corneal topography, Current Opinion in Ophthalmology, 18: 325-333, 2007 ,

The object of the present invention is to develop a solution which overcomes the disadvantages and difficulties of the prior art methods so that measuring and reconstructing curved, reflecting surfaces is more accurate, robust and flexible.

According to the invention, this object is achieved with the method for measuring and reconstructing curved, reflective surfaces, in which the curved, specular surface is illuminated with collimated rays, the light reflected from the curved specular surface is detected, and the structure of the curved, mirrored surfaces is determined by mathematical algorithms. is reconstructed, that the collimated beams from different, defined directions and / or meet at different, defined angles of incidence on the curved, reflective surface, that the reflected light from the curved, reflective surface is detected telecentrically and to reconstruct the curved, specular surface a differential equation system is solved.

The proposed method can in principle be used for measuring and reconstructing curved, reflecting surfaces in various technical fields, such as industrial Quality control are applied. In particular, however, the method is applicable in the clinical diagnosis of ophthalmology for the determination of the biometric data of the cornea of eyes.

The invention will be described in more detail below with reference to exemplary embodiments. Show this

1 FIG. 2: a schematic representation of the illumination of a curved, reflecting surface with a collimated beam, FIG.

2 FIG. 2 is a schematic representation of the telecentric detection of a collimated beam illuminating the curved, specular surface. FIG.

3 FIG. 2: a perspective view of the curved, reflecting surface with a beam reflected as a normal vector, FIG.

4 : A schematic representation of the curved, reflecting surface in plan view, with six beams reflected as normal vectors and

5 : a curved, specular surface reconstructed from 18 normal vectors.

In the proposed method of measuring and reconstructing a curved specular surface, the curved specular surface is illuminated with collimated rays, detects light reflected from the curved specular surface, and reconstructs the curved specular surface structure from it by mathematical algorithms.

According to the invention, the collimated beams strike the curved, reflecting surface from different, defined directions and / or at different, defined angles of incidence. In this case, the rays reflected by the curved, reflecting surface are detected telecentrically and a differential equation system is solved for the reconstruction of the curved, reflecting surface.

For the collimated beams it is valid that either their defined (single-beam) directions or their defined angles of incidence or both can be varied.

The cross section of the collimated beams is in particular so large that in each case the entire, curved, reflecting surface to be reconstructed is illuminated.

This shows the 1 a schematic representation of the illumination of a curved, reflective surface F _GS with a collimated illumination beam BS _K1 from a defined direction. Of the 1 It can be seen that the collimated illumination beam BS _K1 illuminates the entire curved specular surface F _GS . In this case, the collimated illumination beam BS _{K1 is} reflected by the curved, reflective surface F _GS as rays RS ₁₁ to RS _1N in different directions. In addition, in the 1 in addition to the optical axis AO and the axes x, y and z of the Cartesian coordinate system drawn.

Instead of projecting a two-dimensional pattern onto the curved, reflecting surface, it is illuminated over the entire surface with a plurality of collimated rays and only the light portions which are reflected in the direction of the optical axis and thus correspond to the normal vector are detected.

In geometry, a normal vector is a vector that is orthogonal, d. H. is perpendicular or perpendicular to a straight line, curve, plane or even curved surface or a higher-dimensional generalization of such an object.

The necessary number and the distribution pattern of the collimated beams typically depend on the geometric structure of the object to be modeled. For example, the front surface of the cornea of the human eye can be described by spherical models, toric models, bi-conical models or free-form surfaces.

When using the method in ophthalmology, the cornea with the tear film corresponds to the curved, specular surface to be measured.

For eyes with a radius of 7 to 8.5 mm, the cornea typically has a diameter of 11 to 12 mm, with the area around the optical axis being of particular interest. That's why one will central area with a diameter of at least 4 mm, preferably 6 mm and more preferably measured by 8 mm.

For this purpose, the cornea is illuminated with collimated illumination beams from different, defined directions and / or at different, defined angles of incidence, which have a diameter of 2 to 15 mm, preferably 4 to 10 mm. This ensures that the entire cornea to be reconstructed is illuminated.

While for a spherical model 2 collimated beams are sufficient to reconstruct the curved, specular surface, toric and bi-conical models require at least 4, although 6 collimated beams offer much better reproducibility.

It is particularly advantageous here to use 2 sets of 4 or even 3 sets of 6 collimated beams each to obtain more information for the estimation of the asphericity of the human cornea. A set of collimated rays usually has the same angle of incidence.

For the collimated illumination beams, in this case, with respect to the optical axis, angles of incidence between approximately 5 ° and 45 °, but preferably between approximately 6 ° and 30 °, are to be preferred.

If freeform surfaces are used for the description of the front surface of the cornea of the human eye, significantly more (hundreds or even thousands) of collimated rays are required, depending on the number of degrees of freedom of the model for their reconstruction.

The illumination with only two collimated beams from different defined directions and / or under different, defined angles of incidence is preferably effected from opposite directions with the same angles of incidence. As a result, an unambiguous assignment of the reflection beams to the illumination beams is achieved.

When lighting with more than two collimated beams from different defined directions and / or under different, defined angles of incidence, the collimated beams preferably give a symmetrical irradiation pattern, so that here too a clear association between reflection and illumination beams is achieved.

According to the invention, the illumination in the proposed method can take place both successively and simultaneously. Both variants have specific advantages.

While motion artefacts can be ruled out during simultaneous illumination, successive illumination allows clearly defined and assignable reflex points.

According to the invention, the telecentric detection is carried out in such a way that only the rays reflected by the curved, reflecting surface are detected whose direction is parallel to the optical axis, for which purpose an aperture diaphragm is used.

The aperture diaphragm has a correspondingly small opening. This ensures that most of the interfering signals, such as environmental reflections, diffuse reflection, etc., do not even reach the image sensor and could falsify the measurement results.

This shows the 2 a schematic representation of the telecentric detection of a curved, reflecting surface illuminating collimated beam. From the curved reflecting surface F _GS , the collimated illuminating beam BS _{K1 is} reflected in different directions. The reflection beam RS ₁₂ , which corresponds to the normal vector, is reflected in the direction of the optical axis OA and imaged by the telecentric optical system O _TZ onto the optical sensor S _O. For this purpose, the telecentric optic O _TZ has an aperture diaphragm B _A. The illustration of the reflection beams RS ₁₁ and RS ₁₃ to RS _1N reflected in other directions has been omitted for reasons of clarity.

In contrast, the shows 3 a perspective view of the curved, reflective surface with a normal vector reflected beam. Here, only the partial beam BS _K1 . of the collimated illumination beam BS _K1 , which corresponds to the normal vector as the reflection beam RS ₁₂ and from the (not shown) telecentric optical system O _TZ to the (also not shown) optical sensor S _O is shown. By the perspective view it can be seen that the curved, reflective surface F _{GS has} a spherical shape.

α

ist der Winkel zwischen dem Beleuchtungsstrahl und der optischen Achse (z-Achse) und

β

ist der Winkel den die vom Beleuchtungs- und Reflexionsstrahl aufgespannte Fläche mit der x-y-Ebene einschließt.

In the 3 In addition to a coordinate system, the angles α and β are also shown, which will be defined as follows:

α

is the angle between the illumination beam and the optical axis (z-axis) and

β

is the angle that encloses the area spanned by the illumination and reflection beam with the xy plane.

The angle α thus defines the different, defined angles of incidence of the collimated illumination beams and the angle β their direction of irradiation.

The spherical shape of the curved, reflective surface F _GS causes the collimated illumination beams BS _K impinging on different, defined directions and / or under different defined angles of incidence at different locations of the curved, reflective surface F _GS as a normal vector in the direction of the optical axis OA be reflected.

The 4 shows a schematic representation of the curved, reflective surface F _GS in plan view, with six reflected as normal vectors rays. As already mentioned, the angle α defines the angles of incidence of the collimated illumination beams and the angle β their direction of irradiation. Since the six are all on a circular arc as normal vectors, the irradiation of the collimated illumination beam was indeed from different directions β, but each with the same angle of incidence α.

The circles shown on the dashed arc define the reflection vectors RS ₁₁ to RS ₆₁ corresponding to the normal vectors. It can be seen from the numbering of the reflection beams that this is a set of 6 collimated beams which strike the curved reflecting surface F _GS from different, defined directions but at the same angle of incidence.

x, y

zweidimensionale Position auf der x, y-Ebene,

α, β

Einfallswinkel eines kollimierten Strahls,

Assuming that the optical axis of the system is identical to the Z axis of a Cartesian coordinate system and assuming that the surface to be measured can be described by an explicit equation z = f (x, y) It follows that a light beam that is parallel to the optical axis and can be detected by the sensor can then be called a normal vector with the following coordinates:

x, y

two-dimensional position on the x, y plane,

α, β

Angle of incidence of a collimated beam,

For a collimated beam defined by the angles of incidence α and β, the distance between the image sensor and the measured surface is insignificant.

For the detectability of a normal vector, i. H. of a beam reflected in the direction of the z-axis, it is only critical that the curved, specular surface (x, y, z) be illuminated (fully) by the collimated beam.

To reconstruct the curved, reflecting surface, a differential equation system is to be solved.

The differential equation system results from the z components of the normal vectors to be calculated for the individual, collimated beams, each collimated beam having an incident beam with the angles α ₀ , β ₀ and a reflected beam with the angles α ₁ , β ₁ .

According to the invention, the curved, reflecting surface is illuminated with N collimated beams from different, defined directions and / or at different, defined angles of incidence. (x _i , y _i , α _i / 2, β _i ) with i = 1, 2, ... N

As already mentioned, N may be at least 2, preferably 25 and more preferably more than 1000.

und dem Einheitsvektor des Reflexionslichts:

sich deren Summe mit einer Normalisierung auf z-Achse wie folgt ergibt:

wobei φ und ρ für die Normalvektoren definiert sind als:

φ

Winkel zwischen dem Normalvektor und der optischen Achse (z-Achse) und

ρ

Winkel zwischen der x-Achse und der Projektion des Normalvektors auf die x-y-Ebene.

A normal vector can be calculated as the sum of two unit vectors by calculating from the inverse unit vector of the incident light:

and the unit vector of the reflection light:

the sum of which with a normalization on the z-axis results as follows:

where φ and ρ are defined for the normal vectors as:

φ

Angle between the normal vector and the optical axis (z-axis) and

ρ

Angle between the x-axis and the projection of the normal vector on the xy plane.

Next results from the z-components of the normal vectors to be calculated tanφcosρ = (cosα'tanα'cosβ '- cosαtanαcosβ) / (cosα + cosα') tanφsinρ = (cosα'tanα'sinβ '- cosαtanαsinβ) / (cosα + cosα') for telecentric detection with the conditions α '= 0, φ = - α / 2 and ρ = β the following approach: z = f (x, y) ∂f / ∂x = tanφcosρ = -tan α / 2cosβ ∂f / ∂y = tanφsinρ = -tan α / 2sinβ

For the reconstruction of the curved, reflecting surface, a mathematical model is preferably used with a small number of collimated beams in addition to the differential equation system to be solved.

This will allow a mathematical description of the entire curved, reflective surface. The mathematical model to be used is chosen as a function of the known parameters of the respective eye.

This shows the 5 a curved, reflecting surface reconstructed from 18 normal vectors, in the form of 3 sets of 6 collimated beams, with a corresponding coordinate system. As already mentioned, the collimated rays of a sentence have the same angle of incidence.

In addition to spherical or toric models, in the proposed method, assuming a sufficiently large number of measured values, any surface models up to free-form surfaces can be used.

With the solution according to the invention, a method for measuring and reconstructing curved, reflecting surfaces is provided, which overcomes the disadvantages and difficulties of the prior art methods, so that measuring and reconstructing curved, reflecting surfaces is more accurate, robust and flexible ,

Although the proposed method is intended in particular for biometrics in the clinical diagnosis of ophthalmology, it can in principle also be used in other technical fields, such as industrial quality control.

The particular advantages of the proposed method are that any number of collimated illumination beams can be used to illuminate the curved, specular surface from various defined directions and / or at different, defined angles of incidence. Using a mathematical surface model, only 2 collimated illumination beams are sufficient to reconstruct the curved, specular surface.

In addition, not only spherical and toric but any surface models for describing the measured surface can be used.

The essential advantage of the method according to the invention is, however, to be seen in the fact that the use of a telecentric detection optics avoids ambiguity of the reflection points and that the method is combined with the angles of incidence determined from different, defined directions and / or at different, defined angles of incidence. reflecting area incident collimated illumination beams operates independently of distance.

As a result, the focusing requirements are not so critical and the focus area is much larger than with normal camera systems.

Another advantage of the proposed method is the fact that the effects of ambient light and diffuse reflections are largely suppressed by the use of an aperture diaphragm with a small aperture.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• US 5,321,101 [0005]
• US 4685140 A [0007]
• US 5,110,200 A [0008]
• US 5194882 A [0008]
• US 5684562 A [0008]
• US 6116738 A [0008]
• US 5864383 A [0008]
• DE 19857001 A1 [0009]

Cited non-patent literature

• T. Hellmuth et al. [0004]
• T. Swartz et al. [0004]

Claims (16)

A method for measuring and reconstructing a curved specular surface, in which the curved specular surface illuminates with collimated rays, detects the rays reflected by the curved specular surface, and from which the structure of the curved specular surface is reconstructed by means of mathematical algorithms, characterized in that the collimated beams strike the curved, reflecting surface from different, defined directions and / or at different, defined angles of incidence , that the beams reflected from the curved, reflecting surface are detected telecentrically and a differential equation system is solved for the reconstruction of the curved, reflecting surface , A method according to claim 1, characterized in that the cross section of the collimated beams is so large that in each case the entire, to be reconstructed curved, reflecting surface is illuminated. Method according to claims 1 and 2, characterized in that the number of collimated beams used, depending on the geometric structure of the measurement object to be modeled, is at least 2, more than 4 to 6 or even significantly more, up to several 100 or even 1000 , Method according to Claim 3, characterized in that, in addition to the number of collimated beams used, their distribution pattern is also selected as a function of the geometric structure of the measurement object to be modeled and consist, for example, of 2 sets of 4 or 3 sets of 6 collimated beams each, whereby the collimated rays of a sentence have the same angle of incidence. Method according to claims 1 to 4, characterized in that with two collimated beams the illumination takes place from different defined directions and / or under different, defined angles of incidence, preferably from opposite directions with the same angles of incidence. Method according to claims 1 to 4, characterized in that with more than two collimated beams, the illumination takes place from different defined directions and / or under different, defined angles of incidence, wherein the collimated beams preferably give a symmetrical irradiation pattern. Method according to claims 1 to 6, characterized in that the collimated beams impinge on the curved, reflecting surface successively or simultaneously from different, defined directions and / or angles of incidence. A method according to claim 7, characterized in that the illumination of the curved, reflecting surface with collimated rays from different, defined directions and / or under different, defined angles of incidence takes place successively, so that the reflection points are clearly defined and assignable. A method according to claim 7, characterized in that the illumination of the curved, reflecting surface with collimated beams from different, defined directions and / or under different, defined angles of incidence occurs simultaneously to exclude motion artifacts. A method according to claim 1, characterized in that the telecentric detection is performed such that only the reflected from the curved, reflective surface rays are detected, whose directions are parallel to the optical axis, including an aperture stop is used. A method according to claim 1, characterized in that the differential equation system results from the z-component of the normal vectors to be calculated for the individual collimated beams, each collimated beam comprising an incident beam having the angles α ₀ , β ₀ and a reflected beam having the angles α ₁ , β ₁ , where α and β are defined as follows: α Angle between the incident beam and the optical axis z and β Angle enclosing the plane spanned by the incident and reflected beam with the xy plane. A method according to claim 11, characterized in that a normal vector is calculated as the sum of two unit vectors by calculating from the inverse unit vector of the incident light:

and the unit vector of the reflection light:

the sum of which with a normalization on the z-axis results as follows:

where φ and ρ are defined for the normal vectors as: φ angle between the normal vector and the optical axis (z-axis) and ρ angle between the x-axis and the projection of the normal vector onto the xy plane. Method according to claims 11 and 12, characterized in that the z-component of the normal vectors to be calculated tanφcosρ = (cosα'tanα'cosβ '- cosαtanαcosβ) / (cosα + cosα') tanφsinρ = (cosα'tanα'sinβ '- cosαtanαsinβ) / (cosα + cosα') for telecentric detection with the conditions α '= 0, φ = - α / 2 and ρ = β the following solution gives: z = f (x, y) ∂f / ∂x = tanφcosρ = -tan α / 2cosβ ∂f / ∂y = tanφsinρ = -tan α / 2sinβ A method according to claim 1, characterized in that for the reconstruction of the curved, reflective surface with a small number of collimated beams in addition to the differential equation system to be solved, a mathematical model is used. A method according to claim 14, characterized in that the mathematical model to be used is selected as a function of the known parameters of the respective eye. A method according to claims 14 and 15, characterized in that are used as a mathematical model for the front surface of the cornea of the human eye ball models, toric models, bi-conical models or free-form surfaces.

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