Three-dimensional interferometer and method for determining a phase of an electric field

Description

[0001] The invention relates to a method for measuring a light field with a three-dimensional interferometer. The method is suitable, for example, for determining a phase difference at at least one point in an interference region of the three-dimensional interferometer, as well as a method for determining a phase of an electric field in a part of the interference region of the three-dimensional interferometer.

[0002] Interferometers can be differentiated according to their spatial arrangement. Interferometers, such as the Mach-Zehnder interferometer, the Michelson interferometer, or the Sagnac interferometer, are usually two-dimensional interferometers. A distinction between two- and three-dimensional interferometers is provided in the general description.

[0003] Holography is also known in the prior art. Holography is an interferometric technique that allows the amplitude and phase information of a wavefront to be stored, reconstructed, or measured. The result of this technique is called a hologram. In digital holography, the hologram is stored digitally. A holographic camera is a device that records a hologram. In the context of the present application, a holographic camera is understood to be a device that measures the phase, or the phase and amplitude, of an incident field, in particular a light field.

[0004] Furthermore, holographic measurement systems are known in the prior art that serve to measure the amplitude and phase of a light field. The typical setup for holography consists of a light source and a beam splitter that splits the light into a reference beam and an object beam. The object beam is directed onto the object to be measured, reflected / scattered there, and then interfered with the reference beam. This technique requires the presence of a real object; therefore, the object to be imaged cannot be a virtual object.

[0005] Another example of a spatial phase measurement is the Twyman-Green interferometer, a special form of the Michelson interferometer. The Twyman-Green interferometer is a two-dimensional interferometer in which one of the interferometer arms contains the object to be sampled, e.g. a lens, a prism, or a surface. The spatial measurement therefore does not concern the input field, but a property of the interferometer. This is therefore not a spatial measurement of an input field. The interferogram contains information about the spatial surface properties of the object to be sampled. It is characteristic that the object to be sampled is part of the interferometer. In an alternative view of the function, coherent light is reflected from the object to be sampled and caused to interfere with a probe beam generated via the other arm of the Michelson interferometer.Even in this representation, the object to be sampled is part of the interferometric setup and must therefore meet high criteria for mechanical stability, dust-free operation, and general reproducibility. The Twyman-Green interferometer is therefore not an interferometer for local phase measurement of the input field.

[0006] The Twyman-Green interferometer can be thought of as a holographic measurement system in which one of the arms of the Michelson interferometer is used to generate the reference beam. The overlap of the reference beam and the object beam in the Twyman-Green interferometer occurs via the same beam splitter that was used to split the beams into the object and reference beams.

[0007] Both the Twyman-Green interferometer and the holographic measurement system use a reference beam. A reference beam requires the ability to extract light from the light source before it reaches the object. The spatial configuration of the light source, object, and measuring device must be appropriately configured, otherwise the measurement cannot be performed. This type of reference beam provision is called external reference beam provision.

[0008] A three-dimensional interferometer is known from the subsequently published German patent application with the file number DE 10 2014 111 979.7, in which the wave vector of the light beam emanating from the object point in the direction of the device is measured for each point on the object to be imaged. The method used assumes that the light from different object points is incoherent with one another, i.e. that there is no interference between the light from different object points and that there is therefore only coherence between different light beams emanating from the same object point. In this process, the spatial angles of the local position of the individual object points are measured without measuring the wavefront or a comparable quantity. The reason for this is that the overlap of incoherent sources (object points) creates a radiation field that has no defined local phase and therefore no wavefront.A wavefront is defined as points of identical phase in a radiation field. The device is therefore not suitable for interferometric analysis of a wavefront or as a holographic camera. The interferometer disclosed in DE 10 2014 111 979.7 has neither an evaluation unit nor a computer program product.

[0009] US publication US 2004 / 033426 A1 describes an alignment system with a self-referencing interferometer. The interferometer described therein generates two overlapping and relatively rotated images of an alignment mark. The Fourier transforms of the two images are caused to interfere in an image plane, and the intensities are recorded with detectors. Position information is derived from the phase difference between different diffraction orders of the two images. The publication "Digital holography of self-luminous objects by using a Mach-Zehnder setup" by Giancarlo Pedrini et al. (Optics Letters 37, No. 4, pages 713-715) describes a self-referencing interferometer in which a portion of the wavefront of a self-luminous object is filtered and superimposed with the unfiltered wavefront.The US patent US 7,499,174 B2 describes lensless imaging interferometers that produce an image of a laterally extended object.

[0010] It is an object of the present invention to provide a method for measuring a light field using a three-dimensional interferometer. The method should allow for an interferometric determination of the local phase of an incident wave. This determination should be performed with high resolution.

[0011] This object of the invention is achieved by a method for measuring a light field generated by a real object according to patent claim 1. The dependent patent claims define advantageous embodiments.

[0012] The method is intended to solve this problem by using a simple, particularly compact, three-dimensional interferometer. Furthermore, the interferometer used in the method is intended to be cost-effective to manufacture.

[0013] One aspect relates to a method which, using the three-dimensional interferometer, determines a phase difference between a first electric field originating from the first interference arm and a second electric field originating from the second interference arm for at least one point of an interference region of the three-dimensional interferometer.

[0014] Another aspect relates to a method which, using the three-dimensional interferometer, determines a phase of an electric field in a part of the interference region of the three-dimensional interferometer.

[0015] A further aspect relates to a method which, using the three-dimensional interferometer, determines for at least one point of an interference region of the three-dimensional interferometer an amplitude of an interference term or the amplitude of a first or second electric field which originates from the light field passing through the first or second interferometer arm.

[0016] In order to provide a physically correct description of the three-dimensional interferometer used in the method described below, it is necessary to propagate the light field or electric field incident on the interferometer through the interferometer—that is, through both the first interferometer arm and the second interferometer arm—to the detection plane according to general physical equations such as the Huygens, Rayleigh, or Sommerfeld diffraction formulas. This propagates through the interferometer, i.e., through both the first interferometer arm and the second interferometer arm, to the detection plane. A superposition of these two fields at the detection plane can then be calculated. However, it is possible to characterize the interferometer using light fields that satisfy the geometric approximation.

[0017] Geometric optics, which is also called ray optics, can be understood mathematically as a limiting case of wave optics for vanishingly small wavelengths of light.

[0018] This approximation applies in the present case when the wavelengths used are small compared to the dimensions of the components used in the interferometer.

[0019] For any given object point, there is a central ray. However, the interferometer is characterized in the main claim by a single central ray. The central ray depends on the choice of the object point and the detection plane.

[0020] The interferometer is used to measure a light field generated by an object. This means in particular that at least one variable of an electric field is determined. The focus here is on the phase of the electric field. However, a phase and an intensity or an amplitude of the electric field can also be determined. The interferometer is particularly suitable for determining a variable of an electric field, be it a phase or a phase and an intensity of the electric field. The electric field or the intensity can be determined relative to a specified variable, i.e. in comparison to a specified variable. In this case, an absolute variable of the electric field or the intensity does not have to be known. Preferably, an absolute variable of the electric field or the intensity is determined.

[0021] A wavefront can be understood as points of equal phase in the propagation of a wave. The term "measurement of a wavefront" can be used synonymously with a measurement of the phase on a plane, whereby the plane must not be collinear with the direction of propagation, since points of equal phase would be meaningless on such a plane.

[0022] The interferometer comprises a first interferometer arm, a second interferometer arm, a beam splitter, a detection plane, and an overlap device.

[0023] The light of the light field to be measured is at least partially or entirely coherent. The light is particularly preferably coherent light.

[0024] The term partially coherent light refers to the chosen measurement situation. In the case of coherent light, all overlapping wave components are coherent with each other, i.e., there is a temporally fixed relative phase relationship. In the case of partially coherent light, there are overlaps that do not have a completely fixed phase relationship. This occurs when the path length difference of the interfering fields is longer than the coherence length. By changing the path difference between the arms of the interferometer, it is possible to shift the two overlapping fields more or less into the coherence region.

[0025] In particular, one and the same wavefront can be considered a coherent light field in one interferometer setup, while in another it must be considered a partially coherent light source. The causal difference in the interferometer setup is whether the path length differences between the two interferometer arms are longer or shorter than the coherence length of the light source. The coherence length is a property of a light source or light field.

[0026] Preferably, the path length differences occurring in the interferometer setup, measured for rays of the beam of the reference point, are shorter than the coherence length of the incident light field.

[0027] The first interferometer arm can be set up or adjusted such that a first beam passes through it. The second interferometer arm can be set up or adjusted such that a second beam passes through it. Preferably, the first interferometer arm is set up so that a first beam passes through it. Preferably, the second interferometer arm is set up so that a second beam passes through it. Here, the term "a beam passing through an interferometer arm or a device" is preferably understood to mean that none of the rays of the beam are blocked or vignetted by an obstacle. Preferably, no beam is vignetted in the interferometer. The term "beam beam" used here refers to the description of the interferometer in the sense of the main claim.A beam of rays as described in the context of the method according to the invention in the rear part of this application, as well as a beam of rays actually used in the interferometer, can generally be blocked or vignetted by an obstacle.

[0028] Preferably, the second interferometer arm differs from the first interferometer arm at every point between the beam splitter and the overlap device.

[0029] The beam splitter is arranged between an object point on the object, on the one hand, and the first interferometer arm and the second interferometer arm, on the other. The beam splitter is configured so that a beam of light emanating from the object point is split at the beam splitter into the first beam of light and the second beam of light. The beam splitter splits the light field coming from the object, or the beam of light coming from the object point, into two light fields or beams of light, which then pass through the two interferometer arms and are combined at the overlap device so that the two light fields or beams of light interfere in the interference region of the detection plane. The light field is measured in the interferometer by amplitude splitting; wavefront splitting does not occur with respect to the central beam.

[0030] The beam splitter can also comprise or consist of a diffractive optical element (DOE), in particular a grating. A DOE can function as a beam splitter, for example, if the beam incident on the DOE is diffracted into the first and minus-first orders, and the zeroth order is virtually suppressed or not used. In this case, the intensity in the first and minus-first orders is preferably approximately equal.

[0031] In order to measure interference, the optical path length difference between the two interferometer arms must be smaller than the corresponding coherence length of the radiation used.

[0032] The optical path length is the integral of the refractive index along the distance traveled by the radiation. If the refractive index is constant along this path, the optical path length is equal to the product of the refractive index and the distance traveled.

[0033] According to the invention, the object is a real object or, in an unclaimed alternative, can be a virtual object.

[0034] The object point can be any point on the object. To describe the interferometer, a specific object point is chosen without loss of generality, which is also called the reference point. The reference point is chosen so that it lies within the field of view, preferably in the center of the field of view.

[0035] The detection plane is arranged downstream of the first interferometer arm and the second interferometer arm. The detection plane can be set up or adjusted, preferably set up, so that the first beam and the second beam are caused to interfere in an interference region. The interference region is a partial region of the detection plane. The interference region can preferably also be identical to the detection plane. The overlap between the region of the detection plane illuminated by the first beam and the region of the detection plane illuminated by the second beam is preferably as large as possible; preferably, the region illuminated by the first beam is identical to the area illuminated by the second beam. The greater the overlap between the two beams on the detection plane, the more information is obtained about the interference between the two beams.

[0036] The interference region is the area of ​​the detection plane where the first beam and the second beam intersect. Thus, there is an area on the detection plane that is hit by the first beam but not by the second beam, and there is another area on the detection plane that is hit by the second beam but not by the first beam.

[0037] The detection plane is flat. However, according to another embodiment, the detection plane can be replaced by a detection surface that is not flat but curved.

[0038] The overlap device is arranged between the detection plane on the one hand and the first interferometer arm and the second interferometer arm on the other hand.

[0039] Preferably, the beam splitter and the overlapping device are two separate devices.

[0040] The overlapping device is not a reversal of the beam splitter. This can be seen in the fact that a light beam incident on the beam splitter is split into two light beams immediately after the beam splitter. However, two light beams incident on the overlapping device generally do not merge into a single light beam immediately after the overlapping device. Rather, the overlapping device serves the purpose of redirecting two light beams, or more generally, light fields or beam bundles, incident on it in such a way that they cause interference in the interference region of the detection plane.

[0041] It has been stated that two light beams incident on the overlapping device do not usually merge into a single light beam immediately after the overlapping device. There is, however, an exception to this in the case where the central beam is emitted from a central object point. If there is a position of an object point at which the beams of rays incident on the detection plane are equal, this point is called the central object point. It can be shown that the central object point is unique. However, it does not have to be in the field of view of the interferometer used. The central object point is a point for which the central ray emanating from this point produces, after the overlapping device, a first and a second central beam that have the same direction of propagation, i.e., they overlap.

[0042] The overlap device can, for example, comprise a DOE. In this case, the DOE can be used inversely to the normal beam guidance. For example, the first and minus-first diffraction orders can be used as the two beams to be combined, and a normally incident beam can be used as the outgoing combined beam. However, it should be noted that due to the asymmetry between the beam splitter and the overlap device, the same DOE cannot generally be used for the beam splitter and the overlap device.

[0043] In the present application, a beam of rays is understood according to geometric optics to be a number of rays emanating from a point, in particular the object point. Preferably, the beam of rays has a small aperture angle, which is less than 5°, as seen from this point. Other preferred values ​​are 2°, 1°, 0.5°, and 0.1°.

[0044] This definition applies only to the beam of rays which is to be used for the description of the interferometer according to the main claim and according to the alternative formulation.

[0045] For the description of the present main claim, however, only those beams shall be considered which emanate from a selected point, for example the reference point, and which impinge on the detection plane for the selected object point. This does not represent a restriction; one can choose a reference point and a sufficiently small beam without restriction, so that this always applies. It should be noted that, for example, due to imaging errors, the beam emanating from the object point no longer has the property that the rays of the beam emanate from a point after propagation or reflection at beam deflection elements. However, the entirety of these rays should still be referred to as a beam bundle.

[0046] Furthermore, the beam splitter, the first interferometer arm, the second interferometer arm, the overlapping device, and the detection plane are configured or adjustable, preferably configured, such that the following conditions are met. These conditions listed below are restrictions on the relative positioning of the beam splitter, the first interferometer arm, the second interferometer arm, the overlapping device, and the detection plane.

[0047] The first condition is that the beam splitter, the first interferometer arm, the second interferometer arm, the overlap device, and the detection plane can be set up or adjusted, preferably configured, such that there is exactly one central beam emanating from an object point on the object, which is split at the beam splitter into a first central beam and a second central beam. Here, the central beam is part of the beam bundle; the first central beam is part of the first beam bundle and passes through the first interferometer arm, and the second central beam is part of the second beam bundle and passes through the second interferometer arm. Furthermore, the first central beam and the second central beam overlap at a central image point on the detection plane in the interference region.

[0048] For a given object point and for a given position of the detection plane, each beam emanating from this object point has a clearly defined central ray, which can be found as follows: one looks for the light ray of the beam that is split at the first beam splitter into the first central ray and the second central ray and which, after the overlapping device on the detection plane, overlap at one point in the interference area.

[0049] The concept of overlapping two light rays is defined as two light rays overlapping when they pass through a common point, whereby the direction of the individual light rays does not have to be identical, although it can be. One can therefore also say that when two light rays overlap, the directions are irrelevant. The concept of superposition of two light rays is a special case of overlapping in which the two light rays pass through a common point and the respective directions of propagation at this common point are identical. It follows from this that two overlapping light rays also overlap. However, it is not the case that two overlapping light rays always superpose.

[0050] The central ray, and thus the central image point, can be found experimentally as follows. The starting point is that the object point chosen for the construction emits a beam of rays. This beam is restricted to a sub-beam by a movable aperture, e.g., a pinhole aperture (or equivalently, an optical "mark," "obstacle," or "screen") in the beam path between the object point and the two interferometer arms. This sub-beam leads, via the first interferometer arm and the second interferometer arm, to partial illumination of the detection plane, i.e., a restriction of the illumination in the overlap region of the unrestricted beam of rays. If the restricted beam of rays still contains the central ray, there is still an overlap despite the restriction.If the restricted beam no longer contains the central ray, there is no longer any overlap between the partial beams, apart from possible diffraction effects at the aperture. By further moving the aperture, the central ray can be captured by the aperture, resulting in an overlap. Thus, the position of the central ray and the central image point can be determined experimentally.

[0051] It should be emphasized again that the position of the central ray depends on the selected object point. Furthermore, it should be emphasized that one choice of object point leads to a unique characterization of the interferometer. A different choice of object point leads to a different, unique characterization of the interferometer.

[0052] In the following, we will distinguish between two-dimensional and three-dimensional interferometers. Since we are considering interferometers with two interferometer arms, we will not consider one-dimensional interferometers such as the Fabry-Pérot interferometer. Thus, when we talk about interferometers with two interferometer arms, we only consider interferometers that are two-dimensional or three-dimensional.

[0053] In this application, two definitions of two-dimensional interferometers are given. Interferometers that do not fall under these two definitions are considered three-dimensional interferometers.

[0054] According to the first definition, the centers of the elements, in particular the beam deflection elements, of a two-dimensional interferometer are arranged in a plane.

[0055] In this case, a beam splitter or an overlap device is also considered a beam deflection element.

[0056] According to the second definition, a two-dimensional interferometer exists if there is a reference point for which a first plane or plane of incidence, defined by the first and second central rays immediately after the beam splitter, is identical to a second plane or plane of emergence, defined by the first and second central rays immediately before the overlap device.

[0057] All interferometers that fall under one of the above definitions are considered two-dimensional interferometers. All other interferometers are therefore considered three-dimensional interferometers.

[0058] The approximation used to describe the interferometer can be described in more detail at this point. Instead of propagating a complex light field through the interferometer according to Huygens' principle, the following approximations were made. An idealized light field emanating from a chosen reference point is used. It has been shown that for a given reference point and a given detection plane, the central image point and the central ray, i.e., the first central ray and the second central ray, are uniquely determined.

[0059] In addition, a scalar theory is used, specifically a scalar diffraction theory, for which the Helmholtz equation of optics applies, meaning polarization effects are not considered. This approach is particularly correct for unpolarized light, and when only one polarization is present, if the interferometer does not rotate the polarization between the first electric field at the detection plane and the second electric field at the detection plane. This is the preferred configuration and, if not present, can be achieved by an additional polarization-rotating element in the beam path of the first or second interferometer arm.

[0060] Under these conditions, the first electric field on the detection plane can be propagated back along the first central beam to the beam splitter and then propagated forward again along the second central beam to the detection plane to obtain the second electric field. In this approximation, for a given geometry—i.e., for a given interferometer setup—the second electric field on the detection plane can be calculated from a given first electric field on the detection plane. Given the first and second electric fields, one can also calculate how the two electric fields transform into one another.

[0061] In the case of a selected reference point, the electric field propagated by the first interferometer arm for each image point BP1 of the interference region can be referred to as field E1 at image point BP1. In the geometric approximation, the field E1 at point BP1 originates from the light beam traveling from the reference point to BP1. The portion of this light beam before the beam splitter is split into two beams at the beam splitter, the first of which travels via the first interferometer arm to point BP1, and the second of which travels through the second interferometer arm to the detection plane at another image point, called BP2. The second light beam generates field E2 at point BP2. Except for path length differences, and within the framework of the geometric approximation, the field E1 at point BP1 and the field E2 at point BP2 are identical, since the fields originate from the same partial beam before the beam splitter.If the approximation of paraxial optics, also known as Gaussian optics or first-order optics, is applied to the optical elements in the interferometer, the mapping from an arbitrarily chosen point BP1 in the interference region to a point BP2, which is a unique function of point BP1, can, in the most general case, be a projective mapping. In particular, the projective mapping can be an affine mapping.

[0062] Here, a projective map P in two dimensions is defined as follows.

[0063] Each point in the original space and in the image space is given by two coordinates x, y, and x' and y'. For the purposes of projective mapping, each 2-tuple is complemented by a third component equal to 1, i.e., each point corresponds to a vector with three components (x, y, 1) or (x', y', 1).

[0064] All points resulting from multiplication by a number λ are considered equivalent, i.e. (x,y,1) is equivalent to (λx,λy,λ).

[0065] Any three-dimensional vector can be put into the form that the third component is 1, and thus the (x,y,) value can be read in a two-dimensional coordinate system.

[0066] Mathematically speaking, the projective mapping P is a mapping from three-dimensional space to three-dimensional space. However, since we are considering a mapping in two dimensions, we add the third coordinate to the two-dimensional point (x,y) with 1, so that it can be written as follows: (x,y,1). Finally, we apply the 3x3 matrix P and convert the result back to the form (x',y',1). The coordinate pair (x',y') is the result of the projective mapping. Thus, the transformed coordinates can be written as: x ′ = p 11 x + p 12 y + p 13 / p 31 x + p 32 y + p 33 y ′ = p 21 x + p 22 y + p 23 / p 31 x + p 32 y + p 33 where p ij (i and j are numbers from 1 to 3) are the 3x3, i.e. a total of 9, indices of the matrix P. See also Born / Wolf, Principles of Optics, Cambridge University Press, 7th edition, chapter 4.3.1.

[0067] The second condition is that the beam splitter, the first interferometer arm, the second interferometer arm, the overlap device, and the detection plane can be set up or adjusted, preferably configured, such that for each light beam emanating from the object point of the object and forming part of the beam bundle, but not the central beam, there is a first light beam passing through the first interferometer arm and a second light beam passing through the second interferometer arm, which are split from the light beam at the beam splitter and strike the detection plane at different points. Here, the first light beam is part of the first beam bundle, and the second light beam is part of the second beam bundle.

[0068] It should be noted that the first light beam and the second light beam do not always enter the interference zone. There are also cases where either the first light beam or the second light beam does not enter the interference zone.

[0069] According to one embodiment of the interferometer, it has at least two different points of the detection plane mentioned in the second condition, the mutual distance between which is greater than 1 / 1000, preferably 1 / 100, and even more preferably 1 / 10 of the largest dimension of the portion of the detection plane or detector used for detection. The interferometer preferably has an infinite number of such points.

[0070] In the event that the interferometer has a detector in the detection plane which is divided into pixels, the interferometer has at least two different points of the detection plane mentioned in the second condition, the mutual distance of which is greater than 1 pixel, preferably 10 pixels and even more preferably 100 pixels of the detector extent.

[0071] According to one embodiment of the interferometer, 1% of all points in the interference region exhibit this property. Preferably, 5% of all points in the interference region exhibit this property. Further preferred values ​​are 10%, 25%, and 50% of the points in the interference region. If the detection plane has a pixel grid, this condition can be applied analogously to the number of pixels.

[0072] The second condition is defined for every light ray that emanates from the object point of the object and is part of the beam, but not the central ray. The light rays described in this way are generally infinitely numerous, and they strike the detection plane at an infinite number of points. The first light ray strikes the detection plane at an infinite number of points, and the second light ray also strikes the detection plane at an infinite number of points. The second condition creates an assignment for each light ray that is split into a first and a second light beam at the beam splitter. This assignment assigns a first point on the detection plane, which is struck by the first light ray, to a second point on the detection plane, which is struck by the second light ray.This results in a mapping of an infinite number of first points, each struck by a first light beam, to an infinite number of second points, each struck by a second light beam. This mapping is a bijective, i.e., a uniquely reversible mapping of a first region of the detection plane to a second region of the detection plane. This bijective mapping is explained in more detail below in connection with an alternative formulation of the main claim.

[0073] The third condition is that the beam splitter, the first interferometer arm, the second interferometer arm, the overlap device and the detection plane can be set up or adjusted, preferably are set up so that for each image point of the interference region which is not the central image point, there is exactly a third light beam which emanates from the object point, is not the central beam, passes through the first interferometer arm and hits the image point on the detection plane, and there is exactly a fourth light beam which emanates from the object point, is not the third light beam in front of the beam splitter, is not the central beam, passes through the second interferometer arm and overlaps with the third light beam at the image point on the detection plane.

[0074] The third light beam and the fourth light beam are part of the beam bundle before the beam splitter. In the first interferometer arm, the third light beam is part of the first beam bundle. In the second interferometer arm, the fourth light beam is part of the second beam bundle.

[0075] The positions of the third and fourth light beams depend on the choice of the object point and the reference point.

[0076] The subject matter of the main claim of the present invention, which has been described above, can also be described by an alternative formulation. This alternative formulation is more descriptive than the first formulation presented above. However, since it is not clear which formulation is more general, the alternative formulation shall also be presented here, and both shall be considered equivalent for the time being.

[0077] The interferometer according to the alternative formulation is described below. To distinguish the interferometer according to the alternative formulation from the first-described interferometer, it is called the alternative interferometer, whereas the latter is referred to as the first or first-described interferometer.

[0078] Like the first interferometer, the alternative interferometer comprises a first interferometer arm, a second interferometer arm, a beam splitter, a detection plane, and an overlap device.

[0079] The features of the alternative interferometer and the first-described interferometer are identical except for the description of the relative positioning of the beam splitter, the first interferometer arm, the second interferometer arm, the overlap device, and the detection plane. These features were formulated as three conditions in the context of the first-described interferometer. The following describes the alternative representation for all three conditions.

[0080] In the alternative interferometer, the beam splitter, the first interferometer arm, the second interferometer arm, the overlap device and the detection plane can be set up or adjusted, preferably set up so that a first electric field, which originates from the first beam, on the detection plane and a second electric field, which originates from the second beam, on the detection plane, can be converted into one another by a projective image P, wherein the projective image P has exactly one fixed point in the interference region, which is called the central image point.

[0081] The geometric optics approximation applies to both the description of the first interferometer and the description of the alternative interferometer. However, the description of the alternative interferometer also requires the Gaussian optics approximation, also called paraxial optics or first-order optics, because otherwise the relationship between the first and second electric fields cannot be described by a projective mapping.

[0082] One object of the invention is achieved in the alternative formulation by an efficient and controlled superposition of two electric fields that are propagated via the first and second interferometer arms, respectively. One aim here is to maximize the interference region on the detection plane for a fixed beam diameter, i.e. to minimize regions where only one field is present. This is comparable to the task of making a circular disk coincide with itself as closely as possible without identical points lying on identical points. This makes it possible to maximize the interference information. The method chosen for the method described here includes, among other things, a rotation of the two radiation fields against each other.Such a mapping is characterized by the axis of rotation, which means that the projective mapping must have exactly one fixed point, in contrast to a mere translation of the two electric fields, which leads to larger regions where no overlap can occur. A mere translation of the two electric fields relative to each other has no fixed point. A combination of a translation followed by a rotation around a fixed point also has a fixed point.

[0083] This shows that with the chosen technique of one fixed point, larger spatial differences between the light field through the first and second interferometer arm can be achieved than with a device without a fixed point.

[0084] It can also be seen that multiple or infinitely many fixed points mean that the light field overlaps at the same point on the wavefront through the first and second interferometer arms. This means that the corresponding light beam is split but then overlaps with itself again. However, no phase information about the incident light field can be derived from this, because this signal is independent of the phase position of the observation point; it depends only on the path difference.

[0085] In summary, it can be stated that a maximum of the interference information is reached at exactly one fixed point.

[0086] The projective mapping P is preferably uniquely invertible, i.e., bijective. This applies at least in a subregion of the detection plane, preferably across the entire detection plane.

[0087] The projective mapping P depends on the choice of the reference point.

[0088] Since the two electric fields, i.e. the first electric field E1 and the second electric field E2 at the beam splitter are identical, the electric fields on the detection plane can be written as: E 2 x 2 = γ ⋅ E 1 x 1 where the constant complex factor γ takes into account the fact that the attenuation factors in the interferometer arms can be different. If the attenuation factors in the interferometer arms are identical, the magnitude of the factor γ is 1. The functions E2 and E1 are complex functions. In the approximation considered here, the electric fields are not vector fields, but scalar fields. This means that the electric field is a function that assigns a complex function to a three-dimensional position vector x.

[0089] However, equation (1) applies not only to individual values ​​of x 2 and x 1 , but to an infinite number of such values. Here, the mapping P: x 1 → x 2 represents a projective mapping. This can be written as a function as follows: x 2 = P x 1

[0090] The projective mapping has exactly one fixed point x 1F in the interference region, ie for this point the following applies: x 2 = P x 1 F = x 1 F

[0091] The projective image depends on the selected object point or reference point.

[0092] In a real interferometer, vignetting effects of the optical components on the beam deflection elements may need to be taken into account. For the interferometers considered here, it is assumed that the beam bundles are chosen so small that no vignetting effects occur on the optical components or the beam deflection elements.

[0093] The subject matter of the main claim is very easy to understand in the alternative formulation. The light field or the electric field, as it falls on the beam splitter, is split into two paths corresponding to the interferometer arms, in order to then superimpose the two light fields located in the interferometer arms in a controlled manner on the detection plane by shifting and rotating the two light fields relative to each other in a controlled manner. Such a transformation is generally a projective imaging. Because the geometric structure of the interferometer is precisely known, it is also precisely known how the two light fields are transformed into each other. This allows a light field incident on the interferometer to be measured very precisely. The present invention makes it possible to determine the phase of the light field incident on the interferometer according to the invention absolutely up to an additive constant.

[0094] The interferometer preferably has an evaluation unit configured to determine or measure, for at least one point in the interference region of the detection plane, a phase difference between the two light beams interfering there and / or a phase of a light beam incident there. Details of the evaluation method are described below in connection with the method according to the invention. The determination of a phase is generally possible up to an additive constant.

[0095] Preferably, the evaluation unit is configured such that a phase difference between the two light beams interfering there and / or a phase of a light beam occurring there is determined or measured for several points in the interference area.

[0096] Alternatively or in addition to the evaluation unit, the interferometer preferably comprises a computer program product stored on a computer-usable medium, comprising computer-readable program means with which a computer can execute an inventive method described below. The mentioned method is either a method for determining a phase difference at at least one point of an interference region between a first electric field and a second electric field, which interfere at the at least one point, or a method for determining a phase of an electric field in a part of an interference region on a detection plane.

[0097] According to the invention, the interferometer has a detector in the detection plane. The detector has spatial resolution. For this purpose, according to the invention, the detection plane is divided into a plurality of pixels, which can be arranged, for example, like a grid. The technology suitable for detecting the radiation depends on the radiation being observed. In the optical range, CCD or CMOS cameras can be used for this purpose. Cameras with a lock-in function can also be used. The spatial resolution is preferably selected depending on the field of view and taking into account the Nyquist-Shannon criterion such that the phase variation between two evaluation points does not exceed the value of π. The maximum phase variation is given by the largest angle that two rays of interfering beams can subtend, whereby only rays that actually interfere are considered.This angle is related to the angular range that an interferometer can resolve in the object space. This resolved range should preferably correspond to the field of view, i.e. the area from which radiation from the object space can reach the detection area. The detection area here is the area of ​​the detection plane that is recorded by the detector. By means of beam-shaping optical elements in the beam path of the interferometer or in front of the interferometer, it is possible to adapt a given, in particular technologically determined, pixel grid of the detector to the desired field of view. The detectors suitable for an interferometer according to the invention therefore do not have to meet any specified spatial resolution criteria, since it is possible to adapt the interferometer according to the invention to the detector.The great freedom in system selection available here, largely independent of aberration and manufacturing deficiencies, represents a major advantage of the interferometer.

[0098] The evaluation unit is connected to the detector, meaning that the measured values ​​provided by the detector can be queried or read by the evaluation unit. In this case, the evaluation unit calculates the phase difference or phase to be determined by the method according to the invention and makes this information or measured values ​​available, for example, at an interface, so that a user can read this information or measured values.

[0099] FPGAs (Field Programmable Gate Arrays) are preferred as evaluation units for ultra-fast applications.

[0100] According to another embodiment, which is independent of the presence of an evaluation unit, computer systems with graphics processing unit (GPU) evaluation modules or microprocessors with one or more cores can also be used. For most applications, particularly high requirements for the technical equipment of the evaluation unit are not required. Even evaluation with microcomputers, such as Raspberry Pi, is possible, depending on the selected design option.

[0101] Preferably, the first interferometer arm or the second interferometer arm has at least one beam deflection element between the beam splitter and the overlap device. The beam splitter and the overlap device are not included in this calculation. Preferably, each of the two interferometer arms has one or two beam deflection elements.

[0102] A beam deflection element can be defined as a physical object that can at least partially deflect an incident light beam. A beam deflection element can be implemented, for example, as a mirror or a diffractive optical element (DOE). Furthermore, a beam splitter cube is also a beam deflection element.

[0103] According to a further development, at least one beam deflection element comprises a diffractive optical element (DOE), in particular a grating. A DOE can be realized using a very lightweight component.

[0104] Preferably, for the first and second central beams, the length from the beam splitter to the central image point on the detection plane is the same. A measure of this length is the optical path along the described paths. An advantage of this equal path length is that the coherence length of the light used can be shorter.

[0105] A further advantage is the simplified evaluation of the interferograms, since they contain no or fewer diffraction terms. The reason for this is that diffraction effects can compensate for each other during forward and backward propagation, so that in suitable cases, only the difference in path lengths is relevant.

[0106] Preferably, the beam splitter, the first interferometer arm, the second interferometer arm, the overlap device and the detection plane are set up or adjustable, preferably set up so that the beam deflections for a fifth light beam, which is the central beam before the beam splitter and the first central beam after the beam splitter, wherein the fifth light beam is only viewed between a point immediately before the beam splitter and immediately after the overlap device, and for a sixth light beam, which is the central beam before the beam splitter and the second central beam after the beam splitter, wherein the sixth light beam is only viewed between a point immediately before the beam splitter and immediately after the overlap device, the sum is equal to 5, 6 or 7.

[0107] It should be noted that this refers to the total number of beam deflections experienced by both central beams within the interferometer. The beam splitter and the overlapping device are included in the calculation. If only a single beam is deflected in the beam splitter or overlapping device, while the other beam is not deflected, one beam deflection is counted for each element. If a deflection occurs in the beam splitter both between the light beam incident on the beam splitter and the light beam in the first interferometer arm directly after the beam splitter, and between the light beam incident on the beam splitter and the light beam in the second interferometer arm directly after the beam splitter, two beam deflections are counted for the beam splitter.If the overlap device deflects both light beams incident on the overlap device, two beam deflections are counted for the overlap device.

[0108] For an interferometer with equal arm lengths, it can be theoretically proven that for a number of beam deflections equal to four, the first condition, which states that there is a central beam that is split at the beam splitter into the first and second central beams, with the first and second central beams overlapping at the detection plane in the interference region, is satisfied by an infinite number of light beams. Since this contradicts claim 1, which requires that there be exactly one such central beam (for a given object point), it has been proven that an interferometer with equal arm lengths and four beam deflections cannot satisfy claim 1.Furthermore, for the same interferometer, it was demonstrated that for a light beam emanating from the object point of the object and forming part of the beam bundle, but not the central beam, there is a first light beam passing through the first interferometer arm and a second light beam passing through the second interferometer arm, which are split from the light beam at the beam splitter and which strike the detection plane at the same point. Thus, it was also demonstrated that the second condition of the main claim is not met by this interferometer.

[0109] Furthermore, it has been demonstrated theoretically and experimentally that the features of claim 1 are feasible for an interferometer with six beam deflections. Measurements on an already realized prototype can be provided upon request.

[0110] The arm length represents the distance traveled by the first or second central beam from the beam splitter to the central image point on the detection plane. Thus, an equal arm length means that the length for the first and second central beams is the same.

[0111] Preferably, a first plane or plane of incidence, which is given by the first central ray and the second central ray directly after the beam splitter, and a second plane or plane of emergence, which is given by the first central ray and the second central ray directly before the overlap device, are unequal.

[0112] Preferably, a distance between the first plane and the second plane is greater than 0.01 times, preferably 0.1 times, and more preferably 1 times the diameter of the aperture of the beam splitter. This definition applies to parallel planes.

[0113] For non-parallel planes, the angle between the first plane and the second plane is preferably greater than 5°, more preferably greater than 10°, even more preferably greater than 20°, and most preferably greater than 45°.

[0114] Preferably, the interferometer comprises a monolithic optics or structure comprising the beam splitter, the overlap device, and all beam deflection elements in the first and second interferometer arms. All beam deflections occur at the monolithic optics, preferably on the inside of the monolithic optics.

[0115] Preferably, either the first interferometer arm and / or the second interferometer arm has a device for changing an optical path of the corresponding interferometer arm. To carry out the method for determining a phase difference at at least one point in the interference region of the three-dimensional interferometer, it is necessary to change the optical path in an interferometer arm. It is preferred that the change in the optical path be less than or equal to a phase change of 2π. For details of the method, reference is made to the description of the method below.

[0116] The change in the optical path can be achieved by shifting at least one optical element. If this results in a change in the propagation direction, several approaches are available. First, the effect on the propagation direction can be so small as to be negligible. Second, the effect can be taken into account during the evaluation. Third, the change in the propagation direction can be compensated while maintaining the change in the optical path.

[0117] According to a further embodiment, the interferometer preferably further comprises a device for the relative displacement, relative stretching, relative tilting and / or relative rotation of a first light field present on the detection plane, which originates from the first beam, and of a second light field present on the detection plane, which originates from the second beam.

[0118] The device is thus used, for example, to change or transform the first electric field on the detection plane relative to the second electric field on the detection plane such that the transformed first electric field can be described by a projective mapping relative to the original first electric field. The projective mapping is preferably an affine mapping. Any projective mapping is composed of a sequence of displacements, dilations, in particular point dilations, tilting of a plane in space, and rotations. The sequence can also be changed.

[0119] The device for relative displacement, relative tilting and / or relative rotation can be realized by a local displacement or tilting of an optical element, for example a beam deflection element, in the beam path, e.g. in one of the interferometer arms.

[0120] A relative displacement of the first electric field on the detection plane relative to the second electric field on the detection plane is also referred to as "lateral shear." For the present interferometer, which has a spatially resolving detector with pixels, a "lateral shear" of at least one pixel is required; preferably, the "lateral shear" is between 1 and 10 pixels. A relative rotation of the first electric field to the second electric field is also referred to as "rotational shear."

[0121] The different relative position creates an independent data set for an interference term IF and increases the rank of the phase equation.

[0122] By recording an interferogram with a transformed first or second electric field, while the other electric field remains unchanged, an interference signal between the first and second electric fields is provided for each pixel of the detector in the detection plane, thereby obtaining more information about the interference between the two electric fields. This results in an increase in the rank of the quadratic matrix equation. E 1 x i , j ∗ E 2 x i , j ¯ = e iψ i , j E 1 x i , j E 2 x i , j = IF i , j which is explained in more detail below in connection with the method for determining a phase of an electric field in a part of the interference region of the three-dimensional interferometer.

[0123] Here, E1 denotes the first electric field on the detection plane, which originates from the first beam, E2 denotes the first electric field on the detection plane, which originates from the first beam, Ψ denotes the phase difference between E1 and E2, and IF denotes the interference term between the fields E1 and E2. It should make no difference whether the electric field is denoted by E1 or E1. In equation (4), a pixel raster was performed for the location x, which has the indices i and j. Details of equation (4) are described below in connection with the method according to the invention.

[0124] For practical reasons, physical quantities are often denoted with indices in this application. However, the skilled person will understand that a corresponding non-indexed physical quantity may also be used. A corresponding formulation of the corresponding equation can be derived.

[0125] The rank of a system of equations is the number of independent determining equations. If there are fewer determining equations than variables, the system of equations is underdetermined, i.e. the rank is less than the number of independent variables. If the number of independent equations is greater than the number of variables, the system of equations is overdetermined. The system of equations is then solved in such a way that the equations are only approximately satisfied, but the deviation, e.g. the quadratic deviation, is minimized. If the number of independent equations is exactly the same as the number of variables, i.e. if rank is equal, then there is exactly one exact solution to the system of equations.

[0126] For the interferometer according to the invention, equality of rank or overdetermination is preferred for the equation system of equation (4) and the equation systems derived from it. Overdetermined equation systems can be particularly robust against measurement errors and noise.

[0127] The interferometer according to the invention is preferably used as a holographic camera. In this application, the amplitude and phase of a radiation field originating from a real object are measured. This is in contrast to a conventional camera, which only measures the amplitude or, equivalently, the intensity.

[0128] The beam path can be chosen the same in both cases, ie the light source illuminates the object and the reflected light passes through a collecting optics and falls on the camera, where a real image can be created.

[0129] With a conventional camera, it is necessary to create a real image through so-called focusing; with the holographic camera, refocusing is also possible mathematically.

[0130] Through the imaging, the holographic camera measures the phase position of each scattering object point, i.e., the spatial position, down to a multiple of a wavelength. Transparent dielectric layers also change the recorded image, as is known from phase-contrast microscopy. While phase-contrast microscopy only produces a phase contrast, the holographic camera measures the phase as a numerical value.

[0131] The holographic camera can therefore be used on existing optical systems to obtain additional image information.

[0132] The disclosed interferometer can be used for visible light, but in a suitable design also for X-rays, ultraviolet, infrared and far infrared.

[0133] The appropriate technologies must be used for mirrors and gratings during design. Transparent media can be omitted.

[0134] It can also be used with other waves, such as electron waves in an electron microscope and neutron waves. The advantage is that the coherence requirements of the interferometer are low. The path differences must be smaller than the coherence length. It is also possible to work with identical paths.

[0135] The following describes the method for determining a phase difference at at least one point in the interference region of the three-dimensional interferometer, as well as the method for determining the phase of an electric field in a portion of the interference region of the three-dimensional interferometer. These two methods make it possible to measure a light field generated by an object with the interferometer. Therefore, these two methods are extremely important for using the interferometer according to the invention as intended.

[0136] This leads to a difference in the description of the methods compared to the description of the interferometer. In the description of the interferometer, a geometric approximation was used. Furthermore, in the description of the interferometer, only a small, selected beam of rays emanating from a freely chosen reference point on the object was considered. In the description of the methods, this simplified approach is abandoned and an arbitrary radiation field is assumed. This is appropriate, since in reality, the method according to the invention is also carried out in this way.

[0137] The term "ray bundle" is also broader in connection with the method according to the invention, since the object here has a plurality of object points. A beam of rays emanates from each object point. A beam of rays is defined such that all rays emanating from an object point constitute the beam of rays. Thus, the interferometer propagates a superposition of a plurality of beams through the interferometer arms, which are brought into interference on the detection plane in the interference region.

[0138] For this purpose, the so-called fundamental equation of the interferometer is first derived.

[0139] As already explained above, the first electric field, which originates from the first beam, and the second electric field, which originates from the second beam, interfere in the interference region on the detection plane. Accordingly, in the interference region on the detection plane, the measured intensity is the square of the magnitude of a superposition of the first and second electric fields. This can be written as follows: I g = E 1 x i , j + E 2 x i , j 2 where E 1 ( xi,j ) the first electric field at the location xi,j and where E 2 ( x ij ) the second electric field at the location xi,j Here, for the location xi,j a pixel raster with the indices i and j is carried out, where the two indices stand for two orthogonal spatial directions on the detection plane and the interference area, respectively.

[0140] Formula (5) can be calculated as: I g = E 1 x i , j 2 + E 2 x i , j 2 + E 1 x i , j ⋅ E 2 x i , j ¯ + E 1 x i , j ¯ ⋅ E 2 x i , j where E 1 x i , j ∗ E 2 x i , j ¯ = e iψ i , j E 1 x i , j E 2 x i , j = IF x i , j = IF i , j is the equation for the interference term IF. Here, E 2 ( xi,j ) the complex conjugate second electric field.

[0141] For simplicity, the following abbreviations are used: E 1 x i , j = E 1 ij E 2 x i , j = E 2 ij IF x i , j = IF ij

[0142] Using the Rayleigh-Sommerfeld diffraction integral, a relationship between the first and second electric fields on the detection plane can be precisely derived. This assumes exact knowledge of the interferometer, including all apertures, deflections, and distances. It is assumed that the first electric field on the detection plane is known. Using the Rayleigh-Sommerfeld diffraction integral, one can precisely calculate what the field distribution of the first electric field was in the first interferometer arm before the first electric field hit the detection plane. This also allows one to calculate back what the field distribution of the first electric field was in or on the beam splitter. From there, this backward-calculated electric field can be propagated or calculated forward along the second interferometer arm to the detection plane.Thus, if either the first or second electric field is present at the detection level, the other electric field can be uniquely calculated. Thus, a bijective mapping exists between the two electric fields, which can be expressed as a matrix U. The matrix U is also referred to as the propagation matrix. The relationship between the first and second electric fields can be expressed as follows: . E 2 mn = ∑ i , j U mn , ij ⋅ E 1 ij

[0143] Here, the pixel grid (m, n) with the indices m and n preferably describes the same pixel grid (i, j) with the indices i and j for the detection plane, as already explained above. Here, the electric fields are understood as vectors in which all indices are numbered according to a specific order. The order is not important. For example, the entries of the vector can first contain all pixels of the first row and then all pixels of the second row, and so on, until the last row is reached. Thus, the indices i and j of the first electric field E 1 ij be considered as a single index of a vector, which has two indices due to the two-dimensional pixel rasterization. Accordingly, U mn,ija conventional matrix, where the rows are denoted by the two indices m and n and the columns by the two indices i and j. For each interferometer according to the invention, the matrix U must be calculated or determined individually.

[0144] The matrix or mapping U, if appropriately chosen, exhibits all geometric and diffraction effects. U is generally an approximately unitary matrix. For a unitary matrix, the adjoint matrix or Hermitian transpose matrix of the matrix U is equal to the inverse matrix U -1< of the matrix U. The reason why U is generally only an approximately unitary matrix is ​​that during the exact propagation of the electric field, field components can also leave the indexed observation range; these field components are therefore truncated and lost. This is influenced by a suitable choice of the calculation range, the fineness of the indexing.

[0145] If you E 2 ij in formula (7) replaced by the expression from formula (11), we get: IF i , j = E 1 x i , j ∗ E 2 x i , j ¯ = E 1 x i , j ⋅ ∑ m , n U ij , mn ⋅ E 1 mn ¯ = E 1 ij ⋅ ∑ m , n U ij , mn ¯ ⋅ E 1 mn ¯

[0146] If the interference term IF is measured including the phase, ie as a complex quantity, this equation is a quadratic equation in the fields E 1 ij . If one assumes that the indices i, j, m and n in an interferometer range from 1 to 1000, this quadratic equation is very difficult to solve. When multiplying equation (12) by the complex conjugate first electric field E 1 ij , an equation results which, knowing the magnitude of the first electric field E 1 ij is much easier to solve, namely the fundamental equation of the interferometer: IF ij ⋅ E 1 ij ¯ = E 1 ij 2 ⋅ ∑ m , n U ij , mn ¯ ⋅ E 1 mn ¯

[0147] The method for determining a phase difference at at least one point in an interference region of the three-dimensional interferometer and the method for determining the phase of an electric field in a portion of the interference region of the three-dimensional interferometer both revolve around this fundamental equation. For simplicity, the method for determining a phase difference is referred to as the first method, and the method for determining the phase of the electric field is referred to as the second method.

[0148] Equation (13) is, if the magnitude of the first electric field is known E 1 ij a linear equation for the complex, phase-dependent field E 1 ij, which is relatively easy to solve. This requires that the interference term IF has been measured or determined as a complex quantity, the propagation matrix U has been calculated, and the magnitudes of the first and second electric fields are known. Solving equation (13) then yields the first electric field as a complex quantity for at least a portion of the interference region. The second electric field as a complex quantity can then be calculated using equation (11).

[0149] This demonstrates that the respective phases can be calculated from the measured data of the interference term IF by solving a linear homogeneous equation from the amplitudes of the electric fields. This can be achieved, for example, by singular value decomposition (SVD), which requires little numerical effort. This is a key finding of the present invention.

[0150] Here, the phase of the interference term IF is determined using the first method. Knowing the absolute values ​​of the first and second electric fields, the interference term IF can be determined as a complex quantity.

[0151] In the spatial carrier method, depending on the method used, the amplitude is not measured, but only an analysis of the diffraction fringes, or "fringe analysis", is carried out, i.e. a determination of the phase, see e.g. Handbook of optical Metrology, 2nd edition, CRC Press Taylor and Francis Group, Edited by Toru Yoshizawa, Chapter 8, "Speckle Methods and applications", Nandigana Krishna Mohan, Chapter 8.5.1, "Fringe Analysis".

[0152] Using the second method, one can determine the phases of both electric fields. Both methods are explained below.

[0153] Furthermore, an object of the invention is achieved by a method for determining a phase difference Ψ ijat at least one pixel of an interference region between a first electric field and a second electric field which interfere at the at least one pixel, wherein the first electric field originates from a first interference arm and the second electric field originates from a second interference arm.

[0154] The method for determining a phase difference is a first step, which is a prerequisite for the second step, namely the method for determining a phase of an electric field in a part of the interference region of the three-dimensional interferometer, which, starting from the first step, i.e. the method for determining a phase difference, determines a phase of an electric field in a part of the interference region according to the fundamental equation (13).

[0155] When carrying out the method for determining a phase difference, an interferometer according to the invention is preferably used.

[0156] The image point is preferably a point or a pixel of a pixel grid (i, j) of the detection area of ​​the interferometer.

[0157] The phase Ψ ij is a phase difference, given as the difference between the phase of the first electric field Φ1 ij and the phase of the second electric field Φ2 ij and can therefore be expressed as: Ψ ij = Φ 1 ij − Φ 2 ij

[0158] On the one hand, Ψ ij a phase difference between the phases of the interfering electric fields, but on the other hand also a phase of the interference term IF i,j However, phase measurement is usually only possible up to an additive constant.

[0159] Therefore, to determine the phase Ψ ij possible without loss of generality, to Ψ ijto add a constant α.

[0160] Thus, equation (6) can be written as: I g = E 1 ij 2 + E 2 ij 2 + IF ij + IF ij ¯ = E 1 ij 2 + E 2 ij 2 + 2 ⋅ ℜ IF ij = = E 1 ij 2 + E 2 ij 2 + 2 ⋅ E 1 ij E 2 ij ⋅ cos Ψ i , j + α

[0161] For a single pixel with given indices i and j, this equation cannot be solved uniquely for a given α, since the cosine function is not unique, taking every function value between -1 and 1 at two different points. Due to this ambiguity, additional information is required.

[0162] There are essentially two ways to resolve this ambiguity. These two methods, known in the state of the art, are called "temporal phase shifting" and "spatial phase shifting"; see, for example, Handbook of Optical Metrology, 2nd Edition, CRC Press Taylor and Francis Group, Edited by Toru Yoshizawa, Chapter 8, "Speckle Methods and Applications," Nandigana Krishna Mohan, Chapter 8.5.1, "Fringe Analysis." Temporal phase shifting is sometimes referred to as "phase shifting." Spatial phase shifting is sometimes referred to as "carrier phase." When performing the method for determining a phase difference, the so-called first method, the phase shifting method or the spatial carrier method is used according to the invention. Preferably, the phase shifting method and the spatial carrier method are used in combination. This has the advantage of further increasing accuracy.

[0163] In the phase-shifting method, the phase, i.e., the phase difference Ψ, is varied in order to measure the measured function, i.e., the total intensity I g for different values ​​of the cosine function. The phase difference Ψ can be varied by providing the interferometer with a device for changing the relative path length. This can be achieved by the first interferometer arm and / or the second interferometer arm having a device for changing an optical path of the corresponding interferometer arm. Preferably, only one interferometer arm has the device for changing the optical path. A change in the optical path by one wavelength results in a relative phase change of 2π. The phase Ψ used in equation (15) ij changes according to the following replacement: Ψ i , j → Ψ i , j + 2 π Δ s λ where Δs is the change in the optical path and λ is the wavelength used.

[0164] In the carrier-phase method, the interferometer according to the invention is configured so that the phase difference Ψ in a selected direction is a monotonic function of the position x. This can be achieved by setting the overlap of the light rays in the interference region at a minimum angle, i.e., by imposing an additional phase on the phase difference by creating an angle between the central rays. Therefore, the method is also called the carrier-phase method.

[0165] With both methods it is possible to determine the phase Ψ i,j to an additive constant. Furthermore, it is also possible to determine the additive constant to a difference of 2π.

[0166] Preferably, the first method is evaluated for at least two points of the interference region. Preferably, the first method is evaluated for a part of the interference region, in particular the entire interference region.

[0167] In the event that the detection plane of the interference region is divided into pixels, the first method is preferably carried out for two pixels, more preferably for a part of all pixels and particularly preferably for all pixels.

[0168] Preferably, several measurements are carried out in the first method.

[0169] Finally, the phase constant α listed above will be discussed. The phase α is a phase factor which, by definition, is the same for all pixels in the field of view. Relative to the entire field of view, the phase factor α can be uniquely determined up to multiples of 2π. For this purpose, particularly in phase-shifting methods in which the optical path length between the first and second interferometer arms is changed, a position of the path length must be selected as the reference position, to which all phase information subsequently refers. α is uniquely determined for this position by comparing the calculated interferogram for the reference position according to formula (15) with the measurement result, and by determining α such that the agreement is optimal, in particular so that the nodal lines agree.

[0170] It should be noted that the propagation matrix U must be calculated for this reference position, i.e., both the interference term IF and the propagation matrix U must be calculated for the same path length difference. The significance of this correspondence of the reference points can be seen, among other things, in the fact that equation (13) in the second method is only invariant under changes in the α value, or the phase of the interference term IF, if the propagation matrix U is also shifted in phase at the same time.

[0171] The central image point is particularly useful for determining the α value and the precise relative phase position of the arm lengths. The phase difference measured at the central image point is independent of the phase position of the incident light field and is solely the result of the different path lengths of the arms. The central image point is therefore suitable for calibrating the device.

[0172] When using the interference term IF in the fundamental equation, it is always assumed below that the interference term IF and the propagation matrix U refer to the same arm length configuration and that the definition of α for the interference term IF has been done uniquely.

[0173] Furthermore, an object of the invention is achieved by a method for determining a phase of an electric field in a portion of an interference region on a detection plane of a three-dimensional interferometer. The method is preferably suitable for determining a phase of an electric field in a portion of the interference region of the detection plane of the above-described three-dimensional interferometer. This method according to the invention is also referred to as the second method for short. The second method described below comprises four steps.

[0174] In the first step, the intensities or magnitudes of the first and second electric fields are determined for a portion of the interference region. This means that for each point in a portion of the interference region, the magnitude of the first electric field and the magnitude of the second electric field are determined. Since the intensity of the electric field is proportional to the square of the magnitude of the electric field, determining the magnitude of the electric field is equivalent to determining the intensity of the electric field.

[0175] The first step requires determining the magnitude of the first electric field and the magnitude of the second electric field. Alternatively, however, the magnitude of the first or second electric field and the magnitude of the interference term IF can also be determined. Since the magnitude of the interference term is equal to the product of the magnitude of the first electric field and the magnitude of the second electric field, the other of the two electric fields can be calculated from the knowledge of the magnitude of the interference term IF and one of the two electric fields.

[0176] There are several methods or possibilities for determining the magnitudes of the first and second electric fields.

[0177] According to a first possibility, the amplitude of the first or second electric field can be determined by an intensity measurement by blocking the other interferometer arm and measuring the intensity distribution of the pixels on the detection plane. Since the measured intensity is proportional to the square of the desired electric field magnitude, the magnitude of the desired electric field can be obtained in relative units by taking the square root. Alternatively, the proportionality factor can be calculated to obtain the correct magnitude of the desired electric field.

[0178] According to a second possibility, the phase shifting method, in particular the method of "temporal phase shifting", can be used to obtain a complete fit of the measurement signal for different phase positions, ie the total intensity I g = | E 1 ij + E 2 ij | 2< and the magnitude of the interference signal IF, ie |E 1 ij || E 2 ij |. From these two measured values, each of which is a function of two variables, one can solve the quadratic equation | E 1 ij | and | E 2 ij | up to an exchange of the indices 1 and 2.

[0179] Here, the term "a part of the interference region" refers to a subregion of the interference region. The subregion comprises a certain number of points. The subregion does not necessarily have to be connected in the mathematical sense, which means that it can also be disconnected.

[0180] If the interference region or detection plane has a pixel grid, the method can also be performed for a portion of the pixels of this pixel grid. Those skilled in the art know how to evaluate and calculate continuous functions on a pixel grid. For simplicity and greater practical relevance, the equations for the interference region with a pixel grid are given here. However, the method is also intended to be applicable to continuous functions, even if this is not directly reflected in the equations.

[0181] In the second step of the second method, the interference term IF is calculated for the same part of the interference area according to the equation IF ij = E 1 ij ⋅ E 2 ij ⋅ exp i ⋅ Ψ ij certainly.

[0182] Here Ψ ij the difference between the phase Φ1 ij of the first electric field E 1 ij and the phase Φ2 ij of the second electric field E 2 ij . Thus, Ψ ij = Φ1 ij - Φ2 ij (see equation (14)).

[0183] The phase difference Ψ ij is preferably determined using the first method. It should be noted that the phase difference Ψ ij can be determined even without knowledge of the magnitudes of the electric fields, ie the first and second electric fields.

[0184] With the phase difference Ψ ij the interference term IF can be determined as a complex quantity, see equation (17) or (7).

[0185] In the third step of the second method, a propagation matrix U is determined, particularly for the above-mentioned part of the interference region. The propagation matrix U is identical to the matrix U mentioned in connection with the fundamental equation of the interferometer. The components of the propagation matrix U have already been presented and explained above and are written as U mn,ij . An element of the propagation matrix U, ie U mn,ij , indicates how, for a given pixel grid of the interference area, the first electric field E 1 ij at a pixel with indices i and j to the second electric field E 2 ij at a pixel with indices m and n.

[0186] As already explained above, the transformation equation is: E 2 mn = ∑ i , j U mn , ij ⋅ E 1 ij

[0187] The propagation matrix U can preferably be calculated using the Rayleigh-Sommerfeld propagation formula, see Max Born and Emil Wolf, Principles of optics, Cambridge University Press, 8th edition, 2013, Chapter 8.11 Rayleigh-Sommerfeld diffraction integrals, in particular Chapter 8.11.2, formula (14).

[0188] The Rayleigh-Sommerfeld propagation formula is applied as follows. An arbitrary, fictitious first electric field on the detection plane is propagated, taking the geometry into account, along the first interferometer arm back to the beam splitter and then propagated along the second interferometer arm forward into the interference region of the detection plane. This allows a propagation matrix U to be calculated specifically for the concrete setup of the three-dimensional interferometer, which for any first electric field E 1 ij is valid.

[0189] The formulas presented describe the electric fields in the scalar approximation, meaning the polarization of the electric field is not represented in the formulas. This is correct if the light is unpolarized, or if only one polarization is present and the polarization is rectified at the overlap.

[0190] If this is not the case, it must be noted that only light of the same polarization can interfere. This can be achieved by appropriately rotating the polarization in one of the two arms, so that the first and second electric fields on the detector have the same polarization. The interferometer is preferably designed accordingly.

[0191] In the most general case of arbitrary polarizations, one would have to formulate separate equations for each polarization, allowing for a mixture of polarizations during field propagation. This complicates the analysis of the interference patterns, as there is an additional degree of freedom involved, but the procedure is feasible using the methods described.

[0192] In the fourth step of the second procedure, the fundamental equation of the interferometer E 1 ij 2 ⋅ ∑ m , n U ij , mn ¯ ⋅ E 1 mn ¯ = IF ij ⋅ E 1 ij ¯ for the above-mentioned part of the interference region after the complex first electric field E 1 ij Here, the complex first electric field E 1 ij the singular is used. However, the person skilled in the art will understand that in equations (19) and (13) the variables represent the individual components E 1 ijfor each index i and j. In this respect, the plural can also be used here, if one understands that the quantities sought are the first electric field at several points, namely at the pixel positions of the detection plane.

[0193] By complex conjugation one obtains the first electric field E 1 ij . Preferably, by applying the transformation equation (18) the second electric field E 2 ij receive.

[0194] Thus, by the second method, both the phase and the magnitude of both the first and the second electric field have been determined for each point of a part of the interference region.

[0195] The first three steps of the second procedure can be carried out in any order.

[0196] It has already been shown in connection with the first method that the phase difference Ψ ijcan be determined even without knowledge of the magnitudes of the electric fields, i.e., the first and second electric fields. Thus, the first step of the second method is independent of the second step of the second method, so that the order of the first and second steps of the second method can also be reversed. The third step is merely a theoretical calculation, which depends on the geometry of the interferometer used. Thus, the third step is also independent of the first two steps of the second method.

[0197] In the following, statements are made regarding the fundamental equation (19).

[0198] The solution of equation (19) requires knowledge of the magnitude of the first electric field and the complex interference term for each point of the considered part of the interference region and knowledge of the propagation matrix U.

[0199] Under this assumption, equation (19) is a linear equation for the complex first electric fields E 1 ij Here, the plural first electric fields is used, since the first electric field at each point of the considered part of the interference region is meant. Since the right-hand part of equation (19) is also a function of the complex first electric fields E 1 ij , equation (19) can be transformed into a homogeneous equation. The homogeneous equation then has the form that a matrix multiplied by the vector of the complex first electric fields equals a zero vector. Since the pixel spacing (i, j) is preferably identical to the pixel spacing (m, n), the matrix is ​​then a square matrix. In this case, we have a homogeneous linear system of equations whose solution lies in the kernel of the matrix.

[0200] The rank of the linear system of equations described in equation (19) can be increased so that there is exactly one solution to the homogeneous equation (13). This can be achieved by performing additional measurements and simultaneously evaluating them. The kernel of equation (13) thus has dimension 1, or equivalently, there is a solution with eigenvalue 0.

[0201] The mathematical solution to equation (19) can preferably be achieved using singular value decomposition (SVD), which requires little numerical effort. The desired solution to equation (13) is the eigenvector with the smallest singular value in the singular value decomposition. This method is robust against noise or other disturbances in the measured values. In the presence of noise, there may be no solution with exactly the eigenvalue 0. However, equation (19) can also be solved using methods other than singular value decomposition.

[0202] The pixel spacing (i, j) described above is preferably identical to the pixel spacing (m, n). However, this need not necessarily be the case.

[0203] The fundamental equation of the interferometer is formulated above in position space, specifically for a pixel grid of the detection plane. However, it is equivalent to describing this fundamental equation in Fourier space. This has several advantages, for example, the representation of the propagation matrix U is very simple in this case, since the propagation matrix U is a diagonal matrix.

[0204] For this purpose, the propagation matrix U must also be calculated in Fourier space, which is called U ( kx , ky ) and which has the form: U ^ k x k y = exp i ⋅ k z k x k y ⋅ z where z is the path length difference between the two interferometer arms and k z k x k y = 2 π λ 2 − k x 2 − k y 2 is.

[0205] Furthermore, the fundamental equation can also be described in another functional basis appropriate to the problem. For example, Legendre functions, Zernike polynomials, or other orthogonal polynomials from the field of special functions, such as the hypergeometric function, can be chosen.

[0206] Preferably, the second method uses so many points of the interference region that the solution of the fundamental equation E 1 ij 2 ⋅ ∑ m , n U ij , mn ¯ ⋅ E 1 mn ¯ = IF ij ⋅ E 1 ij ¯ is unique up to multiples of the solution. Since equation (19) corresponds to a homogeneous equation, a multiple of a solution is also a solution. All such solutions should be considered equivalent. If only such solutions exist, they are considered unique.

[0207] If equation (19) does not have a unique solution, it may be necessary to produce or record additional interference data. This can be done, for example, by recording additional data for the interference term IF with different relative spatial positions of the first and second electric fields causing the interference. Alternatively, the procedure can also be described as taking two or more images with different projective images using the interferometer.

[0208] The present invention can be realized by the interferometer, a computer program or by a combination of interferometer and computer program.

[0209] Any type of computer system or other device capable of carrying out the methods described herein, i.e., the first and second methods, is suitable. A typical combination of interferometer and computer program / computer program product could be a terminal computer system with a computer program that, when loaded and executed, controls the computer system to carry out the methods described herein. The same applies, for example, to computer applications or applets stored on a chip card.

[0210] Furthermore, one object of the invention is achieved by a computer program. The computer program comprises code portions adapted to perform the steps according to the first and / or second method when said program is loaded into a computer.

[0211] Furthermore, one object of the invention is achieved by a computer program product. The computer program product is stored on a medium usable in a computer and has computer-readable program means with which a computer can execute the first and / or second method.

[0212] Computer program means, or computer program in the present context, any expression in any language, code or notation of a set of instructions designed to perform a particular function on a system having information processing capability, either directly or after one or both of the following operations: (a) conversion into another language, code or notation; (b) representation in another material form.

[0213] The present invention will now be further explained with reference to individual examples and figures. These examples and figures serve only to illustrate the general inventive concept, and should not be construed as limiting the invention in any way. Figure 1 shows a schematic diagram of an embodiment of an interferometer to illustrate the main claim. Figure 2 shows a schematic diagram of an embodiment of an interferometer to illustrate the first condition of the main claim. Figure 3 shows a schematic diagram of an embodiment of an interferometer to illustrate the second condition of the main claim. Figure 4 shows a schematic diagram of an embodiment of an interferometer to illustrate the third condition of the main claim. Figure 5shows a schematic diagram illustrating a projective mapping of the first electric field onto the second electric field. Figure 6 shows a schematic illustration of an embodiment of an interferometer in which both the beam splitter and the overlap device each have a diffraction grating. Figure 7 shows a schematic diagram of an embodiment of the interferometer in which the plane of incidence and the plane of reflection are not identical but are parallel to each other. Figure 8 shows a schematic diagram of an embodiment of an interferometer which can be built compactly and in which the planes of incidence and reflection are perpendicular to each other. Figure 9 shows a schematic diagram of an embodiment of an interferometer with a monolithic structure.

[0214] Figure 1shows a three-dimensional interferometer 100, which interferometrically measures a light field generated by an object 110. As already described in the general description, a special light field is used to characterize the three-dimensional interferometer. This is a beam of rays emanating from an object point 112 of the object 110, which in the Figure 1 is not shown for reasons of clarity. In Figure 1 Only a central ray 114, which is part of the beam bundle, is shown. The central ray 114 extends from the object point 112 to a beam splitter 101, where it is split into a first central ray 120 and a second central ray 121.

[0215] One of the beam splitters 101 can be a beam splitter cube or a glass plate, which preferably has a coating adapted to the radiation used.

[0216] The central beam 114 is amplitude-split at the beam splitter 101. In this process, the second central beam 121 is deflected by a specific angle relative to the direction of the central beam 114, while the first central beam 120 has the same direction as the central beam 114. The first central beam 120 and the second central beam 121 define an incidence plane 154. The incidence plane 154 is graphically indicated by a dashed line. Furthermore, a cross is arranged on the plane, which illustrates the orientation of the incidence plane 154.

[0217] The first central beam 120 runs after the beam splitter 101 in the first interferometer arm 150. The second central beam 121 runs after the beam splitter 101 in the second interferometer arm 152.

[0218] After the beam splitter 101, the first central beam 120 is deflected by a first beam deflection element 171 and a second beam deflection element 172, both arranged in the first interferometer arm 150. After the beam splitter 101, the second central beam 121 is deflected by a first beam deflection element 181 and a second beam deflection element 182, both arranged in the second interferometer arm 152. As already explained above, a certain number of beam deflection elements is necessary to rotate the distribution of the first or second electric field.

[0219] The first central beam 120 is directed by the second beam deflection element 172 in the first interferometer arm 150, and the second central beam 121 is directed by the second beam deflection element 182 in the second interferometer arm 150 to an overlap device 106. From there, the first central beam 120 and the second central beam 121 are directed to a detection plane 131 of a detector 130. As already discussed above, the first central beam 120 and the second central beam 121 meet at a common image point, which is called the central image point 133.

[0220] In general, two light beams incident on the overlapping device do not merge into a single light beam immediately after the overlapping device. This also generally applies to two central beams, i.e., the first central beam 120 and the second central beam 121. However, there is an exception for the case where the central beam 114 is emitted from a central object point (not shown). It can be shown that the central object point is unique, but it does not have to be within the field of view of the interferometer used.

[0221] In the embodiment of the Figure 1 the second central beam 121, which comes from the second beam deflection element 182 in the second interferometer arm 152 and falls onto the overlap device 106, is not deflected at the overlap device 106.

[0222] However, the first central beam 120, which comes from the second beam deflection element 172 in the first interferometer arm 150 and falls onto the overlapping device 106, is deflected at the overlapping device 106 in the direction of the central image point 133 of the directional plane 131.

[0223] The first central beam 120 directly in front of the overlap device 106 and the second central beam 121 directly in front of the overlap device 106 define a plane of incidence 155. The plane of incidence 155 is graphically indicated by a dashed line. The plane of incidence 154 intersects with the plane of incidence 155 in a straight line corresponding to the y-axis of the drawn coordinate system. Here, the plane of incidence 155 is arranged in the xy-plane. The fact that the plane of incidence 154 does not coincide with the plane of incidence 155 corresponds to the definition of a three-dimensional interferometer.

[0224] The first interferometer arm 150 begins at the beam splitter 101 and extends at least to the overlap device 106, but strictly speaking to the detection plane 131. The second interferometer arm 152 begins at the beam splitter 101 and extends at least to the overlap device 106, but strictly speaking to the detection plane 131.

[0225] The three-dimensional interferometer 100 according to the embodiment of the Figure 1 has a total of six beam deflections. The first central beam 120 (which is the central beam 114 before the beam splitter 101) is not deflected at the beam splitter 101, but is deflected once each at the first beam deflection element 171 and the second beam deflection element 172 in the first interferometer arm 150, as well as at the overlap device 106. Thus, the first interferometer arm 150 has a total of three beam deflections.

[0226] The second central beam 121 (which is central beam 114 before the beam splitter 101) is deflected at the beam splitter 101 and once each at the first beam deflection element 181 and the second beam deflection element 182 in the second interferometer arm 152, but not at the overlap device 106. Thus, the second interferometer arm 152 also has a total of three beam deflections. Thus, the first interferometer arm 150 and the second interferometer arm 152 have a total of six beam deflections.

[0227] Figures 2 to 4 show schematic diagrams of an embodiment of an interferometer to illustrate the three conditions of the main claim described in the general description part.

[0228] This illustrates the Figure 2 the first condition, Figure 3 the second condition and Figure 4 the third condition.

[0229] Just as in the Figure 1 can be seen in Figure 2At the upper end, an object 110 with an object point 112, from which a central beam 114 emanates, which is split at a beam splitter 101 into a first central beam 120 and a second central beam 121. The beam splitter 101 is shown in a simplified manner.

[0230] The first interferometer arm 150 is also shown in a highly simplified manner and has only a first beam deflection element 171, which is also shown in a simplified manner. The second interferometer arm 152 is also shown in a highly simplified manner and has only a first beam deflection element 181, which is also shown in a simplified manner.

[0231] The first central beam 120 and the second central beam 121 are directed onto a detection plane 131 of a detector 130 by an overlapping device 106, which is also shown in simplified form.

[0232] The first condition is that the beam splitter 101, the first interferometer arm 150, the second interferometer arm 152, the overlap device 106 and the detection plane 131 can be set up or adjusted, preferably set up, such that there is exactly one central beam 114 emanating from an object point 112 of the object 110, which central beam 114 is split at the beam splitter 101 into a first central beam 120 and a second central beam 121, wherein the first central beam 120 and the second central beam 121 overlap on the detection plane 131 in the interference region 132 in a central image point 133. It can be seen that the first central beam 120 and the second central beam 121 meet at the central image point 133 on the detection plane 131, whereby the propagation directions of the two central beams 120, 121 do not coincide. This corresponds to the definition of overlap.In the exceptional case that the object point 112 is a central object point, the first central ray 120 and the second central ray 121 would have the same direction in the central image point 133, i.e., they would overlap. In the embodiment of the . Figure 2 However, the general case is shown in which the object point 112 is not a central object point.

[0233] It should be emphasized that even in the embodiments of the Figures 2 to 4 the plane of incidence does not coincide with the plane of reflection. Figures 2 to 4 The first beam deflection element 171 in the first interferometer arm 150 and the first beam deflection element 181 in the second interferometer arm 152 represent possibly multiple beam deflection elements. Due to this simplified representation, it is not clearly visible that the plane of incidence does not coincide with the plane of reflection.

[0234] Figure 3illustrates the second condition of the main claim. This states that for each light beam 115 emanating from the object point 112 of the object 110 and being part of the beam bundle, but not the central beam 114, there is a first light beam 125 passing through the first interferometer arm 150 and a second light beam 126 passing through the second interferometer arm 152, which are split from the light beam at the beam splitter 101 and which strike the detection plane 131 at different points 134, 135.

[0235] Compared to the Figure 2 is in the Figure 3Additionally, the light beam 115 is shown, which is part of the (not shown) beam bundle and which is not the central beam 114. The light beam 115 is split at the beam splitter 101 into the first light beam 125 and the second light beam 126, with the first light beam 125 passing through the first interferometer arm 150 and the second light beam 126 passing through the second interferometer arm 152. Thereafter, the first light beam 125 and the second light beam 126 are directed at the overlapping device 106 in the direction of the detection plane 131, wherein the first light beam 125 strikes the detection plane 131 at an image point 134 which is not the central image point 133, and the second light beam 126 strikes the detection plane 131 at an image point 135 which is neither the central image point 133 nor the image point 134.

[0236] Figure 4illustrates the third condition of the main claim. This is that for each image point 134 of the interference region 132 that is not the central image point 133, there is exactly one third light beam 116 that emanates from the object point 112, is not the central beam 114, passes through the first interferometer arm 150, and strikes the image point 134 on the detection plane 131, and there is exactly one fourth light beam 117 that emanates from the object point 112, is not the third light beam 116 before the beam splitter, is not the central beam 114, passes through the second interferometer arm 152, and overlaps with the third light beam 116 at the image point 134 on the detection plane 131.

[0237] Put simply, the third condition states that for each pixel 134 that is not the central pixel 133, there is exactly one third light beam 116 and exactly one fourth light beam 117 that overlap at the pixel 134. Neither the third light beam 116 nor the fourth light beam 117 is the central beam 114. Furthermore, the third light beam 116 passes through the first interferometer arm 150, and the fourth light beam 117 passes through the second interferometer arm 152.

[0238] The third light beam 116 and the fourth light beam 117 are part of the beam bundle upstream of the beam splitter 101. In the first interferometer arm 150, the third light beam 116 is part of the first beam bundle. In the second interferometer arm 152, the fourth light beam 117 is part of the second beam bundle.

[0239] These three conditions illustrated and explained above characterize an interferometer according to the invention.

[0240] According to the alternative formulation of the main claim, the beam splitter, the first interferometer arm, the second interferometer arm, the overlap device and the detection plane can be set up or adjusted, preferably set up so that a first electric field, which originates from the first beam, on the detection plane and a second electric field, which originates from the second beam, on the detection plane, can be converted into one another by a projective image P, wherein the projective image P has exactly one fixed point in the interference region, which is called the central image point.

[0241] Figures 5a to 5d show schematic diagrams illustrating a projective mapping of the first electric field onto the second electric field.

[0242] Starting from Figure 5a, in which a first electric field E1(x) is represented, how by a general projective mapping the second electric field E2(y), which is shown in the Figure 5d is shown, about the intermediate steps of the Figures 5b and 5c can be obtained.

[0243] In Figure 5athe detection plane 131 is shown, on which a field distribution 200 of the first electric field E1(x) is plotted as a function of the location vector x, which has a first component x1 and a second component x2. The coordinate origin is shown in the lower left corner of the detection plane 131. The distribution 200 shown is not a real electric field, but is merely intended to illustrate a spatial structure. The spatial structure shown in this way is striking and can therefore be easily followed by eye in the subsequent transformation steps. For further clarity, the coordinates of the first electric field at location x0, which corresponds to the crosshairs shown, are highlighted.

[0244] A general projective map P can be represented as a sequence of a translation, a rotation about a fixed point and a final projection onto another plane.

[0245] Starting from the Figure 5a is the field distribution of the first electric field E1(x) in the Figure 5b has merely been shifted by a constant vector. This vector has a large x1 and a smaller x2 component.

[0246] Only when it is a complete projective mapping is the transformed field distribution a real field distribution, namely the field distribution of the second electric field on the detection plane 131. However, since the projective mapping is not yet complete at this point, the field distribution must be an intermediate product, which is referred to as field distribution 202 of the transformed first electric field.

[0247] Starting from the Figure 5b the field distribution 202 of the transformed first electric field is rotated around a certain point, so that the field distribution 202 of the transformed first electric field, as shown in the Figure 5cshown.

[0248] The following step of Figure 5c to Figure 5d is the most complicated because it involves a projection. Starting from the Figure 5c the projection is constructed as follows, so that the result of the projection of the field distribution 202 of the Figure 5c in the detection level 131 of the Figure 5d can see.

[0249] The projection of Figure 5c to 5d is illustrated by the following example. A projection can be visualized using a book page, for example. If you look at a book page and rotate it in space and then look at the contour, the contour describes a projection of a rectangle. This is exactly what the step from Figure 5c to Figure 5d . Starting from the Figure 5c the detection plane 131 was shifted and rotated in space, which can be seen at the four corners of the detection plane 131 of the Figure 5ccan be clearly seen. Then, the field distribution 202 of the transformed first electric field was projected onto the original detection plane 131, which resulted in the Figure 5d The field distribution shown in Figure 5d The field distribution depicted can, on the one hand, be understood as a field distribution 202 of the transformed first electric field, the transformation representing the complete projective mapping P, and, on the other hand, this field distribution can also be understood as the field distribution 204 of the second electric field on the detection plane 131.

[0250] The field distribution 204 of the second electric field on the detection plane 131 can be described in the original coordinate system with the components x1 and x2, but also in a transformed coordinate system with the components y1 and y2.

[0251] In Figure 5done can see that the crosshairs, which originally described the first electric field at location x 0 , now describe the second electric field E2 at location y 0 . In this case, the first coordinate system with the components x1 and x2 and the second coordinate system with the components y1 and y2 can be converted into one another by a projective mapping P or the inverse projective mapping P -1< . Since the projective mapping P is bijective according to the invention, there is always an inverse projective mapping P -1< for a projective mapping P.

[0252] Figure 6 shows a schematic illustration of an embodiment of an interferometer in which both the beam splitter and the overlap device each have a diffraction grating. The embodiment of the Figure 6 resembles the representation of the embodiment of the Figure 1 . It differs from the Figure 1however, in that both the beam splitter 101 and the overlap device 106 each have a diffraction grating 192.

[0253] Furthermore, the first interferometer arm 150 has only a first beam deflection element 171, but no second beam deflection element 172. Likewise, the second interferometer arm 152 has only a first beam deflection element 181, but no second beam deflection element 182.

[0254] Here, the diffraction grating 192 of the beam splitter 101 can be used to diffract the incident beam into the first and minus-first orders, while the zeroth order is almost completely suppressed or not used. The intensity in the first and minus-first orders is preferably approximately equal.

[0255] Furthermore, the diffraction grating 192 of the overlap device 106 can be used in reverse to the normal beam guidance. For example, the first and minus-first diffraction orders can be used as the two beams to be combined, and a normally incident beam can be used as the outgoing combined beam. However, any differences between the beam splitter 101 and the overlap device 106 must be taken into account.

[0256] In the embodiment of the Figure 6 the incidence plane 154 and the reflection plane 155 also intersect in a straight line which corresponds to the y-axis.

[0257] Likewise, the total number of beam deflections in the embodiment of the Figure 6 as well as in the design of the Figure 1six. Furthermore, it should be noted that each diffraction grating 192 corresponds to two beam deflections, resulting in a total of four beam deflections. Furthermore, there is one beam deflection each at the first beam deflection element 171 in the first interferometer arm 150 and at the first beam deflection element 181 in the second interferometer arm 152.

[0258] Figure 7 shows a schematic illustration of an embodiment of the interferometer in which the incidence plane 154 and the exit plane 155 are not identical, but are parallel to each other.

[0259] In the design of the Figure 7 What is special is that the plane of incidence 154 and the plane of reflection 155 do not intersect, but they are not identical either. This condition can only be met by two planes if they are parallel to each other, as is the case here.

[0260] The design of the Figure 7has an object 110 with an object point 112 in the lower left corner, from which a central beam 114 strikes a beam splitter 101 designed as a beam splitter cube. While the second central beam 121 is not deflected by the beam splitter 101 and enters the second interferometer arm 152, the first central beam 120 is deflected to the left towards the first beam deflection element 171 in the first interferometer arm 150.

[0261] The plane of incidence 154 is spanned by the first central ray 120 and the second central ray 121 directly after the beam splitter 101.

[0262] The first central beam 120 is deflected in the first interferometer arm 150 by the first beam deflection element 171 from the incident plane 154 upwards toward the second beam deflection element 172 in the first interferometer arm 150. The center of the second beam deflection element 172 is located in the exit plane 155. The first central beam 120 is then deflected by the second beam deflection element 172 toward the overlap device 106, which is designed as a beam splitter, through which it passes undeflected, then impinging on the detection plane 131.

[0263] The second central beam 121, coming from the beam splitter 101, first strikes the first beam deflection element 181 in the second interferometer arm 152 and then the second beam deflection element 182, after which it is reflected by the first beam deflection element 181 onto the overlap device 106. While the first beam deflection element 181 lies in the incidence plane 154, the second beam deflection element 182 is located in the reflection plane 155. After the overlap device 106, the second central beam 121 is deflected onto the detection plane 131.

[0264] In the embodiment of the Figure 7 the exit plane 155 is located above the incidence plane 154. This is indicated by dashed arrows, which are particularly clearly visible on the first central beam 120 between the second beam deflection element 172 and the overlap device 106.

[0265] Furthermore, the design of the Figure 7A total of six beam deflections are provided for both interferometer arms 150, 152. The two beam splitter cubes of the beam splitter 101 and the overlap device 106 each have one beam deflection. The remaining four beam deflections are accomplished by the first beam deflection element 171 and the second beam deflection element 172 in the first interferometer arm 150 and the first beam deflection element 181 and the second beam deflection element 182 in the second interferometer arm 152.

[0266] Figure 8 shows a schematic diagram of an embodiment of an interferometer which can be built very compactly and in which the planes of incidence and reflection are perpendicular to each other.

[0267] The design of the Figure 8 has a central object point in the field of view.

[0268] The design of the Figure 8has an object 110 with an object point 112 at the upper edge, from which a central ray 114 strikes a beam splitter 101 designed as a beam splitter cube. The central ray 114 runs along the negative z-axis.

[0269] While the second central beam 121 is deflected by the beam splitter 101 along the x-axis, the first central beam 120 is not deflected and continues downward along the negative z-axis toward the first beam deflection element 171 in the first interferometer arm 150.

[0270] Since the plane of incidence 154 is spanned by the first central ray 120 and the second central ray 121 directly after the beam splitter 101, the plane of incidence 154 lies in the xz-plane and is thus perpendicular to the xy-plane.

[0271] In the first interferometer arm 150, the first central beam 120, after being reflected from the first beam deflection element 171, travels along the positive z-axis and the negative x-axis to then impinge on the second beam deflection element 172, which is located at the same position in the yz-plane as the first beam deflection element 181 in the second interferometer arm 152.

[0272] After reflection at the second beam deflection element 172, the first central beam 120 strikes an overlapping device 106, designed as a beam splitter cube, which is arranged directly next to the beam splitter cube of the beam splitter 101. The first central beam 120 is deflected by the overlapping device 106 onto the detection plane 131 in the direction of the positive y-axis.

[0273] The second central beam 121 is directed downstream of the beam splitter 101 along the x-axis to the first beam deflection element 181 of the second interferometer arm 152. After reflection at the first beam deflection element 181, the second central beam 121 travels along the negative y-axis and the negative x-axis until it strikes the second beam deflection element 182, whose center is located in the xz plane at the same position as the central image point 133 of the detection plane 131. After reflection at the second beam deflection element 182, the second central beam 121 is directed to the overlap device 106, through which it passes undeflected to strike the detection plane 131.

[0274] Relative to the central object point, the following distances on the central beam are equal for this object point. The distance from the beam splitter 101 to the first beam deflection element 181 is equal to the distance from the second beam deflection element 172 to the overlap device 106. The distances between the respective first beam deflection elements 171, 181 and the respective second beam deflection elements 172, 182 are equal. The distance between the beam splitter 101 and the first beam deflection element 171 is equal to the distance between the second beam deflection element 182 and the overlap device 106.

[0275] The plane of incidence 155 is spanned by the first central ray 120 and the second central ray 121 directly in front of the overlap device 106 and lies in the xy plane. Thus, the plane of incidence 155 is perpendicular to the plane of incidence 154.

[0276] The design of the Figure 8has a total of six beam deflections for both interferometer arms 150, 152. Here, too, the two beam splitter cubes of the beam splitter 101 and the overlap device 106 each have a beam deflection. The remaining four beam deflections are, as in the embodiment of the Figure 7 by the first beam deflecting element 171 and the second beam deflecting element 172 in the first interferometer arm 150 and the first beam deflecting element 181 and the second beam deflecting element 182 in the second interferometer arm 152.

[0277] Figure 9 shows a schematic diagram of an embodiment of an interferometer with a monolithic structure.

[0278] Since the present embodiment of the Figure 9 Since it is difficult to represent three-dimensionally with a monolithic optic, a section in the xy-plane, which is in the Figure 9aand a section in the xz-plane perpendicular to it, which is shown in the Figure 9b shown.

[0279] It should be noted that the arrangement of the beam splitter cubes of the beam splitter 101 and the overlap device 106 and the arrangement of the first central beam 120 and the second central beam 121 are the same as in the embodiment of the Figure 8 To understand how the embodiment of the Figure 9 It is therefore helpful to look at the design of the Figure 8 to visualize.

[0280] The indicated beam splitter cubes of the beam splitter 101 and the overlap device 106 are indicated by dashed lines. The interfaces are integrated into the monolithic optics 210, but they are not optically effective. The partially mirrored inner surfaces 212 and 214 of the monolithic optics 210 are optically effective.

[0281] Thus, the design of the Figure 9 , as well as in the external form of the Figure 8 , the incidence plane 154 in the xz-plane and the reflection plane 155 in the xy-plane perpendicular to it.

[0282] For reasons of clarity, object 110 is connected to object point 112 in the Figure 9 not shown. However, the central beam 114 emanating from the object point 112 can be seen, which strikes the beam splitter 101, which is designed as a beam splitter cube.

[0283] The first central beam 120 results from the central beam 114 by passing through the beam splitter 101 without deflection and running along the negative z-axis (see Fig. 9b) until it is reflected by a part of the monolithic optics 210, which is referred to as the first beam deflection element 171. After the reflection, the first central beam 120 again strikes a part of the monolithic optics 210, which is referred to as the second beam deflection element 172. On this path, the first central beam 120 passes through the partially mirrored inner surface 214. From there, the first central beam 120 is directed to the overlap device 106, from where it is deflected in the direction of the detection plane 131 (see Fig. 9a ).

[0284] The second central beam 121 results from the central beam 114 by reflection at the beam splitter 101 in the direction of a part of the monolithic optics 210, which is referred to as the first beam deflection element 181 of the second interferometer arm 152 (see Fig. 9a). In this way, the second central beam 121 passes through the partially mirrored inner surface 212. From there, the second central beam 121 is reflected to another part of the monolithic optics 210, which is referred to as the second beam deflection element 182. From there, the second central beam 121 is reflected to the overlap device 106, which it passes through undeflected to strike the detection plane 131.

[0285] The beam blocker 216 prevents light from the first interferometer arm 150 from entering the second interferometer arm 152. List of reference symbols

[0286] 100Three-dimensional interferometer 101Beam splitter 106Overlap device 110Object 112Object point 114Central ray 115Light ray of the beam 140, which is not the central ray 114 116Third light ray 117Fourth light ray 120First central ray 121Second central ray 125First light ray 126Second light ray 130Detector 131Detection plane 132Interference region 133Central image point 134Image point 135Image point,which is not the image point 133 150first interferometer arm 152second interferometer arm 154incident plane 155outcident plane 171first beam deflection element in the first interferometer arm 172second beam deflection element in the first interferometer arm 181first beam deflection element in the second interferometer arm 182second beam deflection element in the second interferometer arm 192diffraction grating 200field distribution of the first electric field on the detection plane 202field distribution of the transformed first electric field on the detection plane 204field distribution of the second electric field on the detection plane 210monolithic optics 212partially mirrored inner surface 214partially mirrored inner surface 216beam blocker, E 1 ij first electric field E 2 ij second electric field IFInterference term (i, j)Pixel spacing (m, n)Pixel spacing E 2 ij complex conjugate of the complex second electric field E 2 ij Ψ ij Phase difference Φ1 ij Phase of the first electric field Φ2 ij Phase of the second electric field UPropagation matrix U mn,ij Elements of the propagation matrix U

Claims

1. Method for measuring a light field produced by a real object (110), using a three-dimensional interferometer (100), wherein the object (110) has an object point (112), from which a beam bundle comes, and wherein the interferometer comprises: a first interferometer arm (150), a second interferometer arm (152), a beam splitter (101) arranged between the object point (112) of the object (110) on one side and the first interferometer arm (150) and the second interferometer arm (152) on the other side, a detection plane (131) or detection surface, which is arranged downstream of the first interferometer arm (150) and the second interferometer arm (152), the detection plane (131) or detection surface comprising a detector with pixels, and an overlapping device (106) arranged between the detection plane (131) or detection surface on one side and the first interferometer arm (150) and the second interferometer arm (152) on the other side, the method comprising the following steps: setting up the beam splitter (101), the first interferometer arm (150), the second interferometer arm (152), the overlapping device (106) and the detection plane (131) or detection surface, splitting the amplitude of the beam bundle coming from the object point (112) into a first beam bundle and a second beam bundle at the beam splitter (101), the first beam bundle passing through the first interferometer arm and the second beam bundle passing through the second interferometer arm, combining the first beam bundle and the second beam bundle by means of the overlapping device (106), and causing the first beam bundle and the second beam bundle to interfere in an interference area (132) of the detection plane (131) or detection surface, and measuring, by means of an evaluation unit connected to the detector, for a plurality of image points (133, 134, 135) of the interference area (132) of the detection plane (131) or detection surface, a phase difference (Ψ) between the two light beams interfering there and / or a phase (Φ) of a light beam impinging there, each image point (131, 134, 135) corresponding to one pixel of the detector; wherein the beam splitter (101), the first interferometer arm (150), the second interferometer arm (152), the overlapping device (106) and the detection plane (131) or detection surface are set up in such a way that, for an object point (112) of the object (110), there is exactly one central beam (114) that comes from the object point (112), which central beam is split into a first central beam (120) and a second central beam (121) at the beam splitter (101), without splitting the wavefronts, wherein the central beam (114) is part of the beam bundle, the first central beam (120) is part of the first beam bundle and passes through the first interferometer arm (150), and the second central beam (121) is part of the second beam bundle and passes through the second interferometer arm (152), and wherein the first central beam (120) and the second central beam (121) overlap in a central image point (133) in the interference area (132) on the detection plane (131) or detection surface; and in such a way that, for each light beam (115) that comes from the object point (112) of the object (110) and is part of the beam bundle but is not the central beam (114), there is a first light beam (125) that passes through the first interferometer arm (150) and a second light beam (126) that passes through the second interferometer arm (152), which light beams are split from the light beam (115) at the beam splitter (101) and hit the detection plane (131) or detection surface at different image points (134, 135), and in such a way that, for each image point (134, 135) of the interference area (132) that is not the central image point (133), there is exactly one third light beam (116) that comes from the object point (112), is not the central beam (114), passes through the first interferometer arm (150) and hits the image point (134, 135) on the detection plane (131) or detection surface, and exactly one fourth light beam (117) that comes from the object point (112), is not the third light beam (116) upstream of the beam splitter, is not the central beam (114), passes through the second interferometer arm (152) and overlaps with the third light beam (116) at the image point (134, 135) on the detection plane (131) or detection surface, wherein the third light beam (116) and the fourth light beam (117) are part of the beam bundle upstream of the beam splitter (101).

2. Method according to any one of the preceding claims, wherein the first interferometer arm (150) and / or the second interferometer arm (152) has at least one beam-deflecting element (171, 172, 181, 182) between the beam splitter (101) and the overlapping device (106).

3. Method according to any one of the preceding claims, wherein the beam splitter (101), the first interferometer arm (150), the second interferometer arm (152), the overlapping device (106) and the detection plane (131) or detection surface are set up in such a way that the beam deflections for a fifth light beam, which is the central beam (114) upstream of the beam splitter (101) and is the first central beam (120) downstream of the beam splitter (101), the fifth light beam being considered only between a point immediately upstream of the beam splitter (101) and immediately downstream of the overlapping device (106), and for a sixth light beam, which is the central beam (114) upstream of the beam splitter (101) and is the second central beam (121) downstream of the beam splitter (101), the sixth light beam being considered only between a point immediately upstream of the beam splitter (101) and immediately downstream of the overlapping device (106), are equal to 5, 6 or 7 in total.

4. Method according to any one of the preceding claims, wherein a plane of incidence (154), which is defined by the first central beam (120) and the second central beam (121) directly downstream of the beam splitter (101), and an exit plane (155), which is defined by the first central beam (120) and the second central beam (121) directly upstream of the overlapping device (106), are not the same.

5. Method according to any one of the preceding claims, wherein the first interferometer arm (150) and / or the second interferometer arm (152) has a device for changing an optical path of the interferometer arm (150, 152) in question.

6. Method according to any one of the preceding claims, wherein the interferometer (100) further comprises: a device for the relative displacement, relative stretching, relative tilting and / or relative rotation of a first light field present on the detection plane (131) or detection surface, which first light field originates from the first beam bundle, and a second light field present on the detection plane (131) or detection surface, which second light field originates from the second beam bundle.

7. Method according to any one of the preceding claims, wherein the interferometer (100) is part of a holographic camera.

8. Method according to any one of the preceding claims, which further comprises: determining a phase difference (Ψij) at the at least one image point (134, 135) of the interference area (132) between a first electric field (E1ij) and a second electric field (E2ij), which interfere at at least one image point (134, 135), the first electric field (E1ij) originating from a first interference arm (152) and the second electric field (E2ij) originating from a second interference arm (152).

9. Method according to any one of the preceding claims for determining a phase difference, comprising the following steps: for a part of the interference area (132), determining the intensity or the absolute value of a first electric field (E1ij), which originates from a first interference arm (150), and of a second electric field (E2ij), which originates from a second interference arm (152), for the part of the interference area (132), determining the interference term (IF) according to the equation IF ij = E 1 ij ⋅ E 2 ij ⋅ exp i ⋅ Ψ ij , where Ψij is a phase difference between the phase (Φ1ij) of the first electric field (E1ij) and the phase (Φ2ij) of the second electric field (E2ij), determining a propagation matrix (U), wherein an element of the propagation matrix (U) indicates how, for a given pixel grid of the interference area, the first electric field (E1ij) at a pixel with the indices i and j is transformed into the second electric field (E2ij) at a pixel with the indices m and n, for the part of the interference area (132), solving the equation |E1ij|2· Σm,n Uij,mn · E1mn = IFij · E1ij after the complex first electric field (E1lj), determining the complex second electric field (E2lj) from the complex first electric field (E1lj) and the propagation matrix (U) using the formula E2mn = Σi,j Umn,ij · E1ij, and determining a phase difference Ψij = Φ1ij - Φ2ij in the interference area (132), down to one constant (α), by solving the following equation and adding a phase-shifting method and / or a spatial carrier method: I g = E 1 ij 2 + E 2 ij 2 + IF ij + IF ij ¯ = E 1 ij 2 + E 2 ij 2 + 2 ⋅ ℜ IF ij = = E 1 ij 2 + E 2 ij 2 + 2 ⋅ E 1 ij E 2 ij ⋅ cos Ψ ij + α where Φ1ij is the phase of the first electric field, Φ2ij is the phase of the second electric field, and Ig = |E1(xij) + E2(xij)|2 is the intensity of the superposition of the first and second electric field, measured in the interference area (132).