Device for detecting the amplitude and phase of a wave field

Abstract

Device for detecting the amplitude and phase of a wave field, with a light source for emitting a coherent plane light wave with a first frequency (ω1), with an oscillator to generate a modulation frequency (Δω), with an optical modulator to generate a reference light wave (E LO , ω1'), with a PMD sensor with multiple PMD pixels, each having a first and second integration node (A, B), wherein the PMD sensor and the optical modulator are operated with the modulation frequency (Δω) generated by the oscillator, wherein part of the light emitted by the light source is directed onto the optical modulator and the optical modulator shifts the first frequency (ω1) of the incoming light by the modulation frequency (Δω) so that a reference light wave (E) is present at the output of the optical modulator. LO) with a second frequency (ω1') is available, where a scene or object is illuminated with the first coherent plane light wave and the light wave reflected by the object is an object light wave (E Obj ) forms, where the PMD sensor is connected to the object light wave (E Obj ) and the reference light wave (E LO ) is illuminated in such a way that the angles of incidence or the directions of propagation of both waves are aligned at a predetermined angle (α) to each other and both waves interfere, where the interference is time-varying and has a period corresponding to the frequency shift (Δω) or the modulation frequency (Δω), where the interference is captured alternately by the first and second integration nodes (A,B) in phase synchrony with the modulation frequency (Δω), where, after an integration time for a PMD pixel, a difference signal (AB) is available, from a lateral distribution of the difference signals and taking into account the angles of incidence of the object and reference waves, a laterally resolved amplitude and a laterally resolved phase of the object wave can be determined.

Description

[0001] The application is based on a device for detecting the amplitude and phase of a wave field according to the preamble of the independent claim.

[0002] For example, US Patent 2009 / 0002679 A1 discloses a laser distance measuring device that can determine the distance to an object using a PMD sensor and Doppler tracking. A first optical modulator generates a first modulated light signal, which illuminates a scene. A second optical modulator generates a second modulated light signal, which is fed into an optical coupling element and modulates the light signal reflected from the scene such that the signal received by a PMD sensor is modulated with a Doppler frequency. The PMD sensor generates an amplitude proportional to the power of the received light, depending on the incident light. This signal is fed into a phase-locked loop, which generates an intermediate frequency signal through frequency mixing. From this intermediate frequency signal, a distance signal can be determined, for example, by Fourier transformation.

[0003] US Patent 2019 / 0310372 A1 discloses a method for Doppler correction in optical distance measurement. For this purpose, a first set of distances is determined based on frequency differences between an optical return signal and a first transmitted optical signal with an up-chirp whose frequency increases over time. Similarly, a second set of distances is determined based on frequency differences to a second transmitted optical signal with a down-chirp whose frequency decreases over time. To correctly assign the respective distances from the first and second sets, a cost matrix with values ​​for a cost function is determined. Based on this cost matrix, a matching pair of distances is determined in order to calculate the Doppler effect on the distance from the combination of this pair and to operate a device accordingly.

[0004] German patent DE 10 2014 004 697 A1 discloses a system and method for distance measurement that combines a phase-delay method with multi-wavelength interferometry to enable high resolution over a large measurement range. The system comprises a multi-wavelength holography module for acquiring a holographic measurement data set based on at least one synthetic wavelength. This module has at least two holographic light sources of different wavelengths, whose light beams are each split into an object beam and a reference beam. A key feature is a dispersive diffraction element that tilts the reference beams of the different wavelengths to varying degrees, thereby separating the measurement signals of the individual wavelengths. Additionally, a phase-delay measurement module acquires a coarse distance to extend the uniqueness range of the high-resolution interferometric measurement.

[0005] US Patent 2013 / 0222786 A1 discloses a vector velocimeter for determining the velocity vectors of an object. A laser arrangement emits a measurement beam to illuminate the object, whereupon a signal beam is emitted from it. This signal beam and a reference beam strike a first detector arrangement at an angle and generate a moving interference fringe pattern through interference. The movement of the fringe pattern, which is detected by a first detector arrangement with an array of detector elements, corresponds to a first velocity component of the object in the longitudinal direction of the measurement volume. Additionally, the movement of a speckle pattern can be detected by further detector arrangements to determine further velocity components perpendicular to the first component.

[0006] German patent DE 100 39 422 A1 discloses a method for operating a PMD system in which a PMD sensor is controlled by a modulation signal and a transmitter emits correspondingly intensity-modulated radiation. The method is characterized in that either the modulation signal is varied between at least two modulation frequencies to perform a distance or velocity measurement, or, alternatively, at a fixed modulation frequency, a spectrum is generated from an output signal of the PMD by means of spectral analysis, and a velocity is calculated from the frequency of a significant signal component.

[0007] The object of the invention is to provide a device that enables the detection of the amplitude and phase of a wave field in a short time.

[0008] The problem is solved by the inventive method.

[0009] Advantageously, a device for detecting the amplitude and phase of a wave field is provided, with a light source for emitting a coherent plane light wave with a first frequency, with an oscillator to generate a modulation frequency, with an optical modulator to generate a reference light wave, with a PMD sensor with multiple PMD pixels, each having a first and second integration node, wherein the PMD sensor and the optical modulator are operated at the modulation frequency generated by the oscillator, wherein a portion of the light emitted by the light source is directed onto the optical modulator and the optical modulator shifts the first frequency of the incoming light by the modulation frequency, so that a reference light wave with a second frequency is available at the output of the optical modulator, wherein a scene or object is illuminated with the first coherent plane light wave and the light wave reflected from the object forms an object light wave, wherein the PMD sensor is illuminated with the object light wave and the reference light wave in such a way that the angles of incidence or the directions of propagation of both waves are aligned at a predetermined angle to each other and both waves interfere, where the interference is time-varying and has a period corresponding to the frequency shift or the modulation frequency, wherein the interference is captured alternately by the first and second integration nodes in phase synchrony with the modulation frequency (Δω), whereby a difference signal is available after an integration time for a PMD pixel, from a lateral distribution of the difference signals and taking into account the angles of incidence of the object and reference waves, a laterally resolved amplitude and a laterally resolved phase of the interference applied to the sensor can be determined.

[0010] This approach has the advantage that, even with a single integration phase at the PMD sensor and taking into account the known and predetermined oblique angle of incidence of the reference wave, sufficient data is available to determine the phase and amplitude of a wavefront, particularly an object wave or an apparent interference, incident on the sensor. This enables rapid measurement, allowing, for example, the reliable determination of distances to moving objects.

[0011] They show schematically: Fig. 1 a coherent superposition of a monochromatic object wave and a frequency-shifted monochromatic plane local oscillator wave running obliquely to the z-axis on a CMOS image sensor in the (x,y)-plane at z=0 Fig. 2 Schematic representation of different spatial frequency spectra, Fig. 3 a bichromatic distance measurement, Fig. 4 a monochromatic distance measurement, Fig. 5 a monochromatic distance measurement, Fig. 6 schematically shows a possible evaluation.

[0012] The core idea of ​​the invention is a coherent heterodyne-holographic superposition of an optical wave field and an obliquely incident plane reference wave with detection and reconstruction of the wave field.

[0013] In Fig. Figure 1 shows the coherent superposition of a monochromatic optical wave field and a monochromatic plane wave frequency-shifted by Δω = 2πΔv, which strike an image sensor obliquely to the light waves emanating from the object. The spatial frequency spectrum (v x ,v y The object wave is concentrated around the z-axis, allowing calculations to be performed using a paraxial approximation. For the two positively assumed spatial frequency components (v xLO , v yLO) the plane reference or local oscillator wave should apply vxLO>>|vx|and vyLO>>|vy| and the object wave is assumed to be a paraxial wave field. This condition can essentially be achieved by having the object wave strike the sensor perpendicularly and the reference wave at an oblique angle of incidence.

[0014] The following representation describes the conditions in a scalar approximation, thus assuming in particular linear polarization or the same polarization of the electromagnetic fields.

[0015] The electric field strength at the angles (α x ,α y ) with sin(αxLO)=vxLO / λ and sin(αyLO)=vyLO / λ The monochromatic plane reference or local oscillator wave, propagating obliquely to the z-direction, is, up to a constant phase factor, EL(x,y,z,t)=ELO exp(i(ω+Δω)t−2πi(vxLOx+vyLOy)−ikzz) given, where E LOthe real amplitude of the wave and k z = 2π v z denotes the wave vector component in the z-direction. The electric field of the object or signal wave can be written more generally as E(x,y,z,t)=E0(x,y,z)exp(−iφ(x,y,z))exp(iωt), where E0 (x,y,z) = |E (x,y,z,t)| is the magnitude and φ(x,y,z) is the phase of the signal wave.

[0016] The superposition field in the sensor plane z = 0 is given up to a phase factor by Etot(x,y,z=0,t)=EL(x,y,z=0,t)+E(x,y,z=0,t)=ELO exp(i(ω+Δω)t−2πi(vxLOx+vyLOy)) +E0(x,y,z=0)exp(−iφ(x,y,z=0))exp(iωt).

[0017] The intensity I(x,y,t), as the time-averaged optical energy flux density through the area z = 0, is proportional to the square of the magnitude of the electric field strength. In non-magnetic materials, with refractive index n0, speed of light in a vacuum c0, and dielectric constant ε0, the following relationship generally applies: I(x,y,t) = n0c0ε0 |E|2 and thus follows I(x,y,t) / (n0c0ε0)=|Etot(x,y,z=0,t)|2=ELO2+E02(x,y,z=0) =ELO2+E02(x,y,z=0)+2 ELO Re{E0(x,y,z=0)exp(−2πi(vxLOx+vyLOy)−iφ(x,y,z=0))exp(iΔωt)} =ELO2+E02(x,y,z=0) +2 ELO E0(x,y,z=0)cos(Δωt−2π(vxLOx+vyLOy)−φ(x,y,z=0)).

[0018] The first two terms are constant over time. The interesting third term describes the coherent heterodyne superposition of the object light wave with the frequency-shifted plane local oscillator wave and yields a high-frequency signal whose phase is identical to the phase of the object light wave and whose amplitude is determined by the local oscillator amplitude E. LO can be adjusted.

[0019] With the real part or in-phase component of the total location-dependent complex electric signal field strength Ertot(x,y,z=0)=ELO E0(x,y,z=0)cos(2π(vxLOx+vyLOy)+φ(x,y,z=0)) as well as the imaginary part or quadrature component of the position-dependent complex electric field strength Eitot(x,y,z=0)=ELO E0(x,y,z=0)sin(2π(vxLOx+vyLOy)+φ(x,y,z=0)) This results in strong local oscillator field strength. ELO2>>E02(x,y,z=0) the relationship I(x,y,t) / (n0c0ε0)=ELO2+2 ELO E0(x,y,z=0)cos(2π(vxLOx+vyLOy)+φ(x,y,z=0))cos(Δωt)+2 ELO E0(x,y,z=0)sin(2π(vxLOx+vyLOy)+φ(x,y,z=0))sin(Δωt) or written differently I(x,y,t) / (n0c0ε0)=ELO2+2(Ertot(x,y,z=0)cos(Δωt)+Eitot(x,y,z=0)sin(Δωt)).

[0020] Through the detection process, the complex amplitude distribution of the light wave E0 (x,y,z = 0) exp(-iφ(x,y,z = 0)) is "converted down" into the complex spatial distribution of the high-frequency signal and can thus be completely determined, i.e., in terms of magnitude and phase, for every point in the sensor plane (x,y,z=0).

[0021] For small difference frequencies Δv < 20 Hz, the alternating component can be directly evaluated using a video measurement camera. It is important to ensure that the interference pattern to be recorded does not change during the exposure time of at least one period T = 1 / Δv.

[0022] To record moving objects, significantly higher difference frequencies, preferably around Δv ~ 100 MHz, are required, as offered in particular by synchronously time-integrating active pixel pmd-CMOS sensors. These sensors utilize spatiotemporal modulation of the generated photoelectrons and provide a time-dependent photocurrent characteristic i for each pixel. ph (x,y,t) and luminous flux P(x,y,t) = AI(x,y,t) incident on a pixel of area A of the form iph(x,y,t)=(qη0ℏω+qη1ℏωcos(2πΔvt))P(x,y,t), where q denotes the electron charge and ℏω the photon energy, η0 the static and η1 the dynamic quantum yield, and it was assumed that in the pmd detector each pixel is modulated with the frequency Δv.

[0023] Note: The same transfer function can be achieved with a classic Active Pixel CMOS image sensor with an attached electroabsorption modulator!

[0024] Time averaging over m periods of the high-frequency signal according to <iph(x,y,t)> =(1mT)∫0mTiph(x,y,t)dt According to (10), modulating the pmd detector with cos(Δωt) yields the in-phase component <iphi(x,y,t)> =(n0c0ε0) (qη0ℏωELO2+qη1ℏωELOE0(x,y,z=0)cos(2π(vxLOx+vyLOy)+φ(x,y,z=0))) and accordingly, when the detector is modulated with sin(Δωt), the quadrature component is obtained. <iphq(x,y,t)> =(n0c0ε0)(qη0ℏωELO2+qη1ℏωELOE0(x,y,z=0)sin(2π(vxLOx+vyLOy)+φ(x,y,z=0)))

[0025] Without object light, the signal is simple: <iph0(x,y,t)> =(n0c0ε0)(qη0ℏωELO2).

[0026] Interestingly, a low dynamic quantum efficiency η1 is apparently caused by a strong local oscillator field E. LO can be compensated for.

[0027] The differential measurement signal grows proportionally with the square root of the local oscillator intensity at a constant field strength of the object wave. <iphi,q(x,y,t)> −<iph0(x,y,t)> ∝ELO.

[0028] Taking into account (7) and (8), it can be shown that the real and imaginary parts of the electric field of the object light wave and the superimposed local oscillator wave can be easily determined from the measured sensor signals, since it holds that Ertot(x,y,z=0)=(<iphi(x,y,t)> −<iph0(x,y,t)> )ℏω / (n0c0ε0qη1ELO) and accordingly Eitot(x,y,z=0)=(<iphq(x,y,t)> −<iph0(x,y,t)> )ℏω / (n0c0ε0qη1ELO).

[0029] For stationary wave fields, the measurement of the real and imaginary parts of the complex electric field strength can be performed sequentially in two steps. If the conditions change dynamically, for example due to object movement, beam splitters can be used to generate replicas of the object and reference fields. However, beam splitting introduces angle-dependent distortions, which, although correctable, require a considerable increase in the material cost of the detection process and ultimately make the method less attractive for practical applications. Therefore, the following section demonstrates how the complex electric field strength of the object light in the sensor plane E0 (x,y,z = 0) exp(-iφ(x,y,z = 0)) can be determined solely by measuring the in-phase component according to equation (17) (or alternatively from the quadrature component (18)).

[0030] The inventive method utilizes properties of two-dimensional analytical signals. In general, the (v x ,v y The spatial frequency spectrum of the object light at the sensor's location in the plane z=0 is band-limited according to equation (1), because all waves emanating from a coherently illuminated object reach the finite area of ​​the sensor at a finite angle of incidence significantly less than 90°. Mixing with a plane reference wave with an even larger angle of incidence, i.e., a higher spatial frequency (v), results in a larger spatial frequency (v). xLO , v yLO ), ensures that only frequency components from the first quadrant (v) are present in the spatial frequency spectrum of the superposition signal. xLO > 0,v yLO > 0) are non-zero. Thus, the complex electric superposition field ES(x,y,z=0)=E0(x,y,z=0)exp(−2πi(vxLOx+vyLOy)−iφ(x,y,z=0)) a two-dimensional analytical signal, analogous to a one-dimensional signal with a one-sided spectrum. The real part of the superposition field (19) determines the spatial dependence of the measured signal according to (13) and (16). It holds that 2Re{ES(x,y,z=0)}=2{E0(x,y,z=0)cos(2π(vxLOx+vyLOy)+φ(x,y,z=0))} =exp(2πi(vxLOx+vyLOy)) E0(x,y,z=0)exp(iφ(x,y,z=0)) +exp(−2πi(vxLOx+vyLOy)) E0(x,y,z=0)exp(−iφ(x,y,z=0)) and the two-dimensional Fourier transform is F{Re{ES(x,y,z=0)}}(vx,vy) =δ((vx−vxLO,vy−vyLO)*F{E0(x,y,z=0)exp(iφ(x,y,z=0))} / 2 +δ((vx+vxLO,vy+vyLO)*F{E0(x,y,z=0)exp(iφ(x,y,z=0))} / 2, where ∗ denotes the two-dimensional convolution and δ the two-dimensional δ-function. Due to condition (1) and the translation property of the δ-function, the first term on the right-hand side of equation (21) is only in the first quadrant (v). x > 0,v y > 0) the (v x , v y)-plane is non-zero and the same applies in the fourth quadrant (v x < 0,v y < 0) for the second term of the right-hand side of (21) is different. Using the signum function sgn(vx)={+1 for vx>00 for vx=0−1 for vx<0 This results in the interesting relationship (1+sgn(vx))(1+sgn(vy))F{Re{ES(x,y,z=0)}}(vx,vy) =2δ((vx−vxLO,vy−vyLO)*F{E0(x,y,z=0)exp(iφ(x,y,z=0))}. Inverse Fourier transform yields (according to (20)) F−i{(1+sgn(vx))(1+sgn(vy))F{Re{ES(x,y,z=0)}}(vx,vy)}(x,y,z=0) =exp(2πi(vxLOx+vyLOy))E0(x,y,z=0)exp(iφ(x,y,z=0)), which allows the complex electric field distribution in the sensor plane to be determined taking into account (20) from measured photocurrent signals and the spatial frequencies known from the recording geometry (v xLO ,v yLO ) can be determined according to E0(x,y,z=0)exp(iφ(x,y,z=0))=exp(−2πi(vxLOx+vyLOy))F−i{(1+sgn(vx))(1+sgn(vy))F{Re{ES(x,y,z=0)}}(vx,vy)}(x,y,z=0).

[0031] In Fig. Several spectra are shown schematically to illustrate the considerations described in equations (19) to (24) for determining the complex spatially dependent electric field strength from the measured distribution of the real part. The method is based on the processing of one-dimensional analytical time signals. Determining the real part of the spatially dependent field strength is a special feature, not only because it allows measurements down to the quantum noise limit in practice, but also because it enables excellent short-time or high-frequency measurements down to the single-digit nanosecond or gigahertz range, and is therefore well suited for recording moving objects.In simpler versions of the method, spatially resolved depth determinations in the z-direction, i.e. in the direction of view, are possible, for example using holographic two-wavelength methods or velocity measurements in the z-direction by exploiting the Doppler effect.

[0032] The complex electric field strength distribution E(x,y,z=0) measured by the pmd sensor in the plane z = 0 is related to the field strength distribution E(x,y,z = z0) in the plane z = z0 > 0 via the diffraction integral. In a paraxial approximation, the following holds: E(x0,y0,z=z0)=(exp(ikz0)iz0λ)∫∫−∞∞E(x,y,z=0)exp(ik2z0[(x0−x)2+(y0−y)2])dxdy, where k = 2π / 2 = ω / c0 is the vacuum wavenumber. A converging lens with refractive index n0, thickness Δz, focal length f in the sensor plane z = 0 results in an additional quadratic phase rotation with the amplitude transmission factor. t(x,y)=exp[ik(n0−1)Δz]exp(−ik2f[x2+y2]), where the first factor accounts for an additional constant phase shift on the optical axis. The electric field strength distribution in the rear focal plane of the lens, i.e., for z0 = f, is thus E(x0,y0,z=f)=(exp(ikf)iλf)exp[ik(n0−1)Δz]exp(−ik2f[x02+y02])∫∫−∞∞E(x,y,z=0)exp(−i2πλf[xx0+yy0])dxdy.

[0033] This is, except for the constant factor 1 / (iλf) and a phase factor that depends only on the coordinates (x0,y0), the Fourier transform of the field distribution in the lens plane z = 0. The intensity distribution in the focal plane, i.e., in the far-field image plane, is correspondingly... I(x0,y0,z=f)=|E(x0,y0,z=f)|2=1 / (λf)2|∫∫−∞∞E(x,y,z=0)exp(−i2πλf[xx0+yy0])dxdy|2.

[0034] The intensity distribution in other planes can be calculated in a similar way. From the measured field distribution E(x,y,z = 0), one obtains, so to speak, "subsequently" in every other image plane, thus allowing the object to be reconstructed in its entire depth.

[0035] The coherent recording of optical interference fields generally requires that the object and recording system remain stationary. More precisely, the interference pattern to be recorded should not smear during exposure. Displacements Δz ≪ λ are required in the direction of the optical axis, i.e., in the z-direction. For difference frequencies of Δ v At approximately 100 MHz, integration times of mT = m / Δv ≈ 100 ns can be achieved. Therefore, the following applies to the maximum permissible speeds in the z-direction v: z mT ≪ 1 or (with λ = 1µm, m=10) v z ≪ 10 m / s = 36 km / h

[0036] On the other hand, movements in parts of the object occur at velocities of v z = 10 m / s to Doppler frequency shifts of δv = vv z / c0 = 10 MHz. Such axial velocities can be detected with detector systems tuned to modified difference frequencies (Δv + δv).

[0037] One challenge is capturing fine structures in the interference pattern in the (x,y) sensor plane, which is largely determined by the lateral extent of the illuminated object. The smallest structures Δx are generated by object rays incident on the sensor at the largest angle Δθ, measured to the optical z-axis. The superposition of these waves with the strong axial local oscillator wave produces patterns with a period Δx = λ / sin Δθ.

[0038] The considerations presented here demonstrate that coherent image acquisition systems already offer an attractive alternative for one-dimensional applications with near-point or only weakly divergent object illumination. These systems are characterized by extremely high receive sensitivity, approaching the quantum noise limit. Object illumination is achieved with minimal intensity, resulting in extremely low energy consumption. This also ensures maximum eye safety. In addition to acquiring three-dimensional spatial coordinates (z-coordinate acquisition is not discussed here!), axial velocities can be directly detected as a function of location. The analyses performed for the near-infrared range are fully transferable to the visible spectral range. Diode laser systems with high electro-optical conversion efficiencies exceeding 30% and high coherence lengths well over 100 m are available for all of these ranges.The frequency shift required for the investigated heterodyne technique can be very conveniently realized by the use of acousto-optic modulators, which can also be advantageously used to generate short optical pulses and pulse trains with minimum pulse lengths of 5 ns.

[0039] The object is illuminated with two spatially coherent light waves with different frequencies ω1 and ω2 but the same amplitudes E. 10 (x,y,z) = |E1 (x,y,z,t)| and E2 (x,y,z) = |E2 (x,y,z,t)|, where the difference frequency (ω1 - ω2) / 2π ≈ 100 MHz is typically in the high-frequency range. We choose a plane reference or local oscillator wave that travels obliquely to the z-axis. EL(x,y,z,t)=ELO exp(i(ω1+Δω)t−2πi(vxLO1x+vyLO1y)−ikzLO1z)+ELO exp(i(ω2+Δω)t−2πi(vxLO2x+vyLO2y)−ikzLO2z) and add more v yLO1 = v yLO2 = 0 and v xLO1 = v xLO2 = v xLOFor the sake of simplicity, we consider an object concentrated directly around the z-axis in the far field at z ≈ -z0 / 2, |z0| ≫ λ, from which after Fig. a backscattered paraxial wave emanates, which appears as a plane wave near the sensor at z=0. E(x,y,z,t)=|E0|exp(−ikz1(z−z0)+iω1t)+|E0|exp(−ikz2(z−z0)+iω2t) This can be approximated, and z0 takes into account the additional path the light has to travel to illuminate the object. The sensor dimensions are typically small compared to |z0|, and the intensity in the sensor plane z = 0 is I(x,y,t)={EL(x,y,z=0,t)+E(x,y,z=0,t)}{EL(x,y,z=0,t)*+E(x,y,z=0,t)∗}, where the superscript asterisk * denotes the notation for forming a complex conjugate. Calculation using (21) and (22) yields I(x,y,t)=ELO2(2+2cos(ω2−ω1)t)+2ELO|E0|(cos(kz1z0−Δωt+2πvxLOx)+cos(kz1z0+(ω1−ω2−Δω)t+2πvxLOx))+2ELO|E0|(cos(kz2z0−Δωt+2πvxLOx)+cos(kz2z0+(ω2−ω1−Δω)t+2πvxLOx))+|E0|2(2+2 cos[(kz2−kz1)z0+(ω2−ω1)t]).

[0040] Bei der Kreisfrequenz Do ist das Signal EΔω(t)=2ELO|E0|[cos(kz1z0−Δωt+2πvxLOx)+cos(kz2z0−Δωt+2πvxLOx)] =2ELO|E0|[cos(kz1z0+2πvxLOx)cosΔωt+sin(kz2z0+2πvxLOx)sinΔωt] +2ELO|E0|[cos(kz2z0+2πvxLOx)cosΔωt+sin(kz2z0+2πvxLOx)sinΔωt].

[0041] Kreuzkorrelation, dh Multiplication with cosΔωt und Zeitintegration über eine ganze Zahl m von Perioden T = 1 / Δω liefert das Signal (1mT)∫0mTEΔω(t)cosΔωt dt =2ELO|E0| cos[(kz2−kz1)z0 / 2] cos[2πvxLOx+(kz2+kz1)z0 / 2] ≈2ELO|E0| cos[(ω2−ω1)z0 / 2c0] cos[2πvxLOx+ω1z0 / 2c0], where c0 denotes the speed of light in a vacuum. On the synchronous sensor, according to the characteristic curve (11), a cosinusoidally modulated fringe pattern results on the uniform background intensity, which is determined primarily by the strong reference wave; more precisely, a beat signal in the x-direction, whose period is 1 / v. xLO depends on the spatial frequency of the reference wave, and its amplitude changes periodically with the depth coordinate z0 of the object. Accordingly, according to (13), the following relationship is obtained for the in-phase component of the measured photocurrent: <iphi(x,y,t)> =<iphi(x)> =(n0c0ε0)(qη0ℏω2 ELO2) +(qη1ℏω2 ELO|E0| cos(kz2−kz1)z0 / 2) cos[2πvxLOx+(kz2+kz1)z0 / 2]).

[0042] Without object light, the photocurrent signal is determined solely by the strong local oscillator light. <iph0(x,y,t)> =(n0c0ε0)(qη0ℏω2 ELO2), which is to be assumed to be constant in time and space across the sensor area. The contrast K of the spatial beat signal in the x-direction is given by K(z0)=<iphi,max(x)> −<iphi,min(x)><iphi,max(x)> +<iphi,min(x)> =(|E0| / ELO)|cos((kz2−kz1)z0 / 2)|.

[0043] Fig. Figure 3 shows a method for determining the depth coordinate of a point-illuminated, diffusely scattering object using a pmd image sensor. A spatially coherent bichromatic laser source is used for illumination. The scattered light is recorded using a heterodyne holographic method.

[0044] The contrast can be used to precisely determine z0, if, as in Fig. The process is schematically represented. The bichromatic light backscattered by the object is superimposed on a partial surface of the sensor with the bichromatic reference wave (21) and simultaneously on another separate part of the sensor with the monochromatic partial wave of (21), which is caused by ELmon(x,y,z,t)=ELO exp(i(ω1+Δω)t−2πi(vxLO1x+vyLO1y)−ikzLO1z) is given. Evaluation with the modified reference wave as in (27) to (29) yields the superimposed wave (21) on the plane reference wave and evaluated simultaneously with (26). The modified signal corresponding to equation (26) is (1mT)∫0mTEΔω,mon(t)cosΔωt dt =ELO|E0|cos[2πvxLOx+kz1z0]=ELO|E0|cos[2πvxLOx+ω1z0 / 2c0].

[0045] The same applies to the measured photocurrent signal. <iphi,mon(x,y,t)> / (n0c0ε0) =(qη0ℏω2 ELO2)+(qη1ℏω2 ELO|E0|cos[2πvxLOx+kz1z0]), and with the modified contrast K mon (z0) = (|E0| / E LO) z0 can be determined from the ratio K(z0) / Kmon(z0)=|cos((kz2−kz1)z0 / 2)|=|cos[(ω2−ω1)z0 / 2c0] determine. The contrast changes periodically with z0. The condition for maximum contrast is z. 0,2m = 2mπc0 / (ω2 - ω1), where m is an integer. Minimal contrast is found for z 0,(2m+1) = (2m + 1)πc0 / (ω2 - ω1).

[0046] The distance measurement method described for point-like object illumination can be easily extended to one-dimensional illumination patterns (stripes, lines) and two-dimensional area illumination. Spatially resolved distance determination remains guaranteed for convex objects as long as the waves incident on the sensor from the object and the plane reference wave satisfy condition (1).

[0047] Fig. Figure 4 shows a setup in which an object wave E reflected from an object Obj and a frequency-shifted reference wave E LoThe signal is directed towards a sensor and made to cause interference. The sensor, which is designed as a demodulator, demodulates the interference signal applied to it.

[0048] As already shown in formula (5): Etot=EObj+ELo Etot=aeiφ(x,y,z)e−iωt+Aeikre−iωt−iΔωt and for the intensity: I≈|E2|=a2+A2+Re 2aAeiφ(x,y,z)e−iωteikze−iωt−iΔωt with ≫ a I(x,y,t)≈A2+2A(x,y)cos(Δωt−φ(x,y)−kr)

[0049] According to the invention, to determine object distances, it is provided that the real part is detected with a sensor that demodulates the signal at the beat frequency Δω.

[0050] In the example according to Fig. 5. A laser emits coherent light with a frequency ω1 towards an object. To form a reference wave or frequency ω1', a portion of the light emitted by the laser is directed onto an optical modulator, here an acousto-optic modulator AOM, which shifts the incoming laser frequency by a modulation frequency Δω applied to the optical modulator. ω1'=ω1'+Δω

[0051] The sensor is designed as a synchronous demodulator and preferably operates according to a photon mixing principle or PMD principle and has an array or at least a row of light-time-of-flight pixels that detect the interference of the reference and object wave at the sensor in phase synchrony with the modulation frequency Δω.

[0052] Starting from the phase-synchronously determined signals and preferably taking into account the angle of incidence of the reference wave, the phase and amplitude of the object wave hitting the sensor or the apparent interference can be determined, from which, for example, the object wave can be calculated and, if necessary, object distances can also be determined.

[0053] The modulation frequency Δω is generated using a modulator designed in such a way that the modulation frequency Δω is provided to the optical modulator and the demodulator or PMD sensor in phase synchrony or possibly shifted by a predetermined phase position.

[0054] Fig. Figure 6 schematically shows one possible evaluation method. Fig. Figure 6 shows the embodiment according to Fig.5 in simplified form. The laser and demodulator are spaced apart by a distance L. In this example, an object at a distance d is illuminated as a point source, and the backscattered object wave interferes with the reference wave at the demodulator. As a result of the demodulation, the difference signal (AB) shows an interference pattern of the time-varying component of the detection signal. A spatial frequency spectrum, typically exhibiting two maxima, can be generated by Fourier transformation.

[0055] However, the arrangement according to the invention suppresses a maximum, so that an angle of incidence δ of the object wave can be determined starting from the detected maximum. Based on the distance between transmitter and receiver L and the angle of incidence δ, the angle of incidence can be calculated using standard triometric considerations. d=L⋅tan(π2−δ) determine a distance to the object.

Claims

[1] Device for detecting the amplitude and phase of a wave field, with a light source for emitting a coherent plane light wave with a first frequency (ω1), with an oscillator to generate a modulation frequency (Δω), with an optical modulator to generate a reference light wave (E LO , ω1'), with a PMD sensor with multiple PMD pixels, each having a first and second integration node (A, B), wherein the PMD sensor and the optical modulator are operated with the modulation frequency (Δω) generated by the oscillator, wherein part of the light emitted by the light source is directed onto the optical modulator and the optical modulator shifts the first frequency (ω1) of the incoming light by the modulation frequency (Δω) so that a reference light wave (E) is present at the output of the optical modulator. LO) with a second frequency (ω1') is available, where a scene or object is illuminated with the first coherent plane light wave and the light wave reflected by the object is an object light wave (E Obj ) forms, where the PMD sensor is connected to the object light wave (E Obj ) and the reference light wave (E LO ) is illuminated in such a way that the angles of incidence or the directions of propagation of both waves are aligned at a predetermined angle (α) to each other and both waves interfere, where the interference is time-varying and has a period corresponding to the frequency shift (Δω) or the modulation frequency (Δω), where the interference is captured alternately by the first and second integration nodes (A,B) in phase synchrony with the modulation frequency (Δω), where, after an integration time for a PMD pixel, a difference signal (AB) is available, from a lateral distribution of the difference signals and taking into account the angles of incidence of the object and reference waves, a laterally resolved amplitude and a laterally resolved phase of the object wave can be determined.

Images