DE102021132521A1 - Arrangement for recording short-term holograms - Google Patents

Abstract

Arrangement for recording short-term holograms of moving objects using heterodyne technology, consisting ofa) a laser system that emits coherent light with a first frequency (ω1),b) with a beam splitter that splits the coherent light pulse for object illumination and a second one by a difference frequency (Δω > δω ) generates a frequency-shifted reference light pulse,c) with a first beam path, in which the reference light pulse (ω+Δω) falls as a plane wave obliquely on a sensor at an angle of incidence (αLO), measured against the optical axis,d) with a second Beam path for illuminating an object with the coherent light pulse of the first frequency,e) with a spatial frequency filter system which ensures that light rays scattered back from the object hit the image sensor at a maximum angle αmaxwith αmax<αLO.

Description

The invention is based on an arrangement for recording short-term holograms of moving objects using heterodyne technology according to the preamble of claim 1.

The recording of holograms using reference and object waves is well known.

The object of the invention is to further develop the hologram recording technique with regard to moving objects.

The object is solved by the arrangement according to claim 1.

1. a) einem Lasersystem, das kohärente Lichtimpulse mit Kreisfrequenz ω und spektraler Bandbreite δω < 2π/ Δt emittiert,
2. b) einem Strahlteiler, der einen ersten Strahl zur Objektbeleuchtung und einen zweiten um Δω > δω frequenzverschobenen zweiten Strahl zur Referenz erzeugt,
3. c) einem ersten Strahlengang bei der Lichtfrequenz ω+ Δω, der als ebene Welle schräg unter dem Winkel α_LO, gemessen gegen die optische Achse auf den Sensor fällt,
4. d) einem zweiten Strahlengang zur Beleuchtung eines Objekts mit einer Lichtfrequenz ω,
5. e) einem Raumfrequenzfiltersystem, das dafür sorgt, dass vom Objekt rückgestreute Lichtstrahlen mit einem maximalen Winkel α_max mit α_max < α_LO auf den Bildsensor treffen.

An arrangement for recording short-term holograms of moving objects in heterodyne technology is advantageously proposed, consisting of

1. a) a laser system that emits coherent light pulses with angular frequency ω and spectral bandwidth δω < 2π/ Δt,
2. b) a beam splitter, which generates a first beam for object illumination and a second beam, frequency-shifted by Δω > δω, for reference,
3. c) a first beam path at the light frequency ω+ Δω, which falls on the sensor as a plane wave at an angle α _LO, measured against the optical axis,
4. d) a second beam path for illuminating an object with a light frequency ω,
5. e) a spatial frequency filter system, which ensures that light rays scattered back from the object hit the image sensor at a maximum angle α _max with α _max < α _LO .

The invention is explained in more detail with reference to the figures.

• 1 eine kohärente Überlagerung einer monochromatischen Objektwelle und einer frequenzverschobenen monochromatischen schräg zur z-Achse laufenden ebenen Lokaloszillatorwelle auf einem CMOS-Bildsensor in der (x,y)-Ebene bei z=0,
• 2 Schematische Darstellung verschiedener Raumfrequenzspektren,
• 3 eine bi-chromatische Entfernungsmessung,
• 4 eine mono-chromatische Entfernungsmessung,
• 5 eine alternative mono-chromatische Entfernungsmessung,
• 6 ein Beispiel einer bi-chromatischen Entfernungsmessung gemäß 3,
• 7 ein Beispiel mit einer Raumfrequenzfilterung mit Hilfe von Blenden.

They show schematically:

• 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,
• 2 Schematic representation of different spatial frequency spectra,
• 3 a bi-chromatic distance measurement,
• 4 a mono-chromatic distance measurement,
• 5 an alternative mono-chromatic distance measurement,
• 6 an example of a bichromatic distance measurement according to 3 ,
• 7 an example with spatial frequency filtering using apertures.

The core idea of the invention is a coherent heterodyne-holographic superimposition of an optical wave field and an obliquely incident planar reference wave with a detection and reconstruction of the wave field

und die Objektwelle wird als paraxiales Wellenfeld angenommen. Die folgende Darstellung beschreibt die Verhältnisse in skalarer Näherung, setzt also insbesondere lineare Polarisation der elektromagnetischen Felder voraus.In 1 shows the coherent superposition of a monochromatic optical wave field and a monochromatic plane wave frequency-shifted by Δω = 2πΔv, which strikes an image sensor at an angle to the light waves emanating from the object. The spatial frequency spectrum (v _x ,v _y ) of the object wave is concentrated around the z-axis, so that it can be calculated in a paraxial approximation. For the two assumed positive spatial frequency components (v _xLO , v _yLO ) of the plane reference or local oscillator wave should hold $$v_{xLO}\gg \left|v_x\right|\text{and}{v}_{yLO}\gg \left|v_y\right|$$

and the object wave is assumed to be a paraxial wave field. The following representation describes the conditions in a scalar approximation, i.e. it assumes in particular linear polarization of the electromagnetic fields.

(2) schräg zur z-Richtung ausbreitenden monochromatischen ebenen Referenz- oder Lokaloszillator-Welle ist bis auf einen konstanten Phasenfaktor durch $$E_L\left(x,y,z,t\right)=E_{LO}\text{exp}\left(i\left(\omega +\Delta \omega \right)t-2\pi i\left({\nu }_{xLO}x+{\nu }_{yLO}y\right)-i{k}_{z}z\right)$$

gegeben, wobei E_LO die reelle Amplitude der Welle und k_z = 2π v_z die Wellenvektorkomponente in z-Richtung bezeichnen. Das elektrische Feld der Objekt- oder Signal-Welle lässt sich ganz allgemein schreiben als $$E\left(x,y,z,t\right)=E_0\left(x,y,z\right)\text{exp}\left(-i\phi \left(x,y,z\right)\right)\text{exp}\left(i\omega t\right),$$

wobei E₀ (x, y, z) = |E(x,y,z,t)| der Betrag und φ(x,y,z) die Phase der Signalwelle sind.The electric field strength at the angles (α _x , α _y ) with $$\text{sin}\left(a_{xLO}\right)=v_{xLO}/\lambda \text{and sin}\left(a_{yLO}\right)=v_{yLO}/\lambda$$

(2) Monochromatic plane reference or local oscillator wave propagating obliquely to the z-direction is through up to a constant phase factor $$E_L\left(x,y,\mathrm{e.g},t\right)=E_{LO}\text{ex}\left(i\left(\omega +\Delta \omega \right)t-2\pi i\left(v_{xLO}x+v_{yLO}y\right)-i{k}_{\mathrm{e.g}}\mathrm{e.g}\right)$$

given, where E _LO denotes the real amplitude of the wave and k _z = 2π v _z denote the wave vector component in z-direction. The electric field of the object or signal wave can be generally written as $$E\left(x,y,\mathrm{e.g},t\right)=E_0\left(x,y,\mathrm{e.g}\right)\text{ex}\left(-i\phi \left(x,y,\mathrm{e.g}\right)\right)\text{ex}\left(i\omega t\right),$$

where E ₀ (x,y,z) = |E(x,y,z,t)| are the magnitude and φ(x,y,z) the phase of the signal wave.

The superimposed field in the sensor plane z = 0 is given by except for a phase factor $$\begin{array}{l}{E}_{tOt}\left(x,y,\mathrm{e.g}=\mathrm{0,}t\right)=E_L\left(x,y,\mathrm{e.g}=\mathrm{0,}t\right)+E\left(x,y,\mathrm{e.g}=\mathrm{0,}t\right)\\ =E_{LO}\text{ex}\left(i\left(\omega +\Delta \omega \right)t-2\pi i\left(v_{xLO}x+v_{yLO}y\right)\right)\\ +E_0\left(x,y,\mathrm{e.g}=0\right)\text{ex}\left(-i\phi \left(x,y,\mathrm{e.g}=0\right)\right)\text{ex}\left(i\omega t\right).\end{array}$$

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 absolute value of the electric field strength. In non-magnetic materials, the general relationship I(x,y,t) = n ₀ c ₀ ε ₀ |E| applies with refractive index n ₀ , vacuum speed of light c ₀ and dielectric constant ε ₀ ² and it follows $$\begin{array}{l}I\left(x,y,t\right)/\left(n_0{c}_0{e}_0\right)={\left|E_{tOt}\left(x,y,\mathrm{e.g}=\mathrm{0,}t\right)\right|}^2={\mathrm{<figure-callout\; id="2"\; label="E\; L\; O"\; filenames="DE102021132521A1\_0061.png,DE102021132521A1\_0062.png"\; state="\{\{state\}\}">E</figure-callout>}}_{LO}^{}+{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0^2\left(x,y,\mathrm{e.g}=0\right)\\ =E_{LO}^2+{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0^2\left(x,y,\mathrm{e.g}=0\right)\\ +2E_{LO}Re\{E_0\left(x,y,\mathrm{e.g}=0\right)\text{ex}(-2\pi i\left(v_{xLO}x+v_{yLO}y\right)-i\phi (x,y,\mathrm{e.g}=\\ 0))\text{ex}\left(i\Delta \omega t\right)\}\\ =E_{LO}^2+E_0^2\left(x,y,\mathrm{e.g}=0\right)\\ +2E_{LO}{E}_0\left(x,y,\mathrm{e.g}=0\right)\text{cos}\left(\Delta \omega t-2\pi \left(v_{xLO}x+v_{yLO}y\right)-\phi \left(x,y,\mathrm{e.g}=0\right)\right).\end{array}$$

The first two terms are constant in time. The interesting third term describes the coherent-heterodyne superimposition of the object light wave with the frequency-shifted planar local oscillator wave and supplies a high-frequency signal whose phase is identical to the phase of the object light wave and whose amplitude can be adjusted by the local oscillator amplitude E _LO .

sowie Imaginärteil bzw. Quadraturkomponente der ortsabhängigen komplexen elektrischen Feldstärke $$E_{itot}\left(x,y,z=0\right)=E_{LO}{E}_0\left(x,y,z=0\right)\text{sin}\left(2\pi \left({\nu }_{xLO}x+{\nu }_{yLO}y\right)+\phi \left(x,y,z=0\right)\right)$$

ergibt sich für starke lokale Oszillatorfeldstärke $E_{LO}^2\gg E_0^2\left(x,y,z=0\right)$

die Beziehung $$\begin{array}{l}I\left(x,y,t\right)/\left(n_0{c}_0{\epsilon }_0\right)=E_{LO}^2\\ +2E_{LO}{E}_0\left(x,y,z=0\right)\text{cos}\left(2\pi \left({\nu }_{xLO}x+{\nu }_{yLO}y\right)+\phi \left(x,y,z=0\right)\right)\text{cos}\left(\Delta \omega t\right)\\ +2E_{LO}{E}_0\left(x,y,z=0\right)\text{sin}\left(2\pi \left({\nu }_{xLO}x+{\nu }_{yLO}y\right)+\phi \left(x,y,z=0\right)\right)\text{sin}\left(\Delta \omega t\right)\end{array}$$

oder anders geschrieben $$\begin{array}{l}I\left(x,y,t\right)/\left(n_0{c}_0{\epsilon }_0\right)\\ =E_{L0}^2+2\left(E_{rtot}\left(x,y,z=0\right)\text{cos}\left(\Delta \omega t\right)+E_{itot}\left(x,y,z=0\right)\text{sin}\left(\Delta \omega t\right)\right).\end{array}$$

With real part or in-phase component of the entire location-dependent complex electrical signal field strength $$E_{\mathrm{right}tOt}\left(x,y,\mathrm{e.g}=0\right)=E_{LO}{E}_0\left(x,y,\mathrm{e.g}=0\right)\text{cos}\left(2\pi \left(v_{xLO}x+v_{yLO}y\right)+\phi \left(x,y,\mathrm{e.g}=0\right)\right)$$

and imaginary part or quadrature component of the location-dependent complex electric field strength $$E_{itOt}\left(x,y,\mathrm{e.g}=0\right)=E_{LO}{E}_0\left(x,y,\mathrm{e.g}=0\right)\text{sin}\left(2\pi \left(v_{xLO}x+v_{yLO}y\right)+\phi \left(x,y,\mathrm{e.g}=0\right)\right)$$

results for strong local oscillator field strength ${\mathrm{<figure-callout\; id="2"\; label="E\; L\; O"\; filenames="DE102021132521A1\_0061.png,DE102021132521A1\_0062.png"\; state="\{\{state\}\}">E</figure-callout>}}_{LO}^{}\gg {\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0^2\left(x,y,\mathrm{e.g}=0\right)$

the relationship $$\begin{array}{l}I\left(x,y,t\right)/\left(n_0{c}_0{e}_0\right)=E_{LO}^2\\ +2E_{LO}{E}_0\left(x,y,\mathrm{e.g}=0\right)\text{cos}\left(2\pi \left(v_{xLO}x+v_{yLO}y\right)+\phi \left(x,y,\mathrm{e.g}=0\right)\right)\text{cos}\left(\Delta \omega t\right)\\ +2E_{LO}{E}_0\left(x,y,\mathrm{e.g}=0\right)\text{sin}\left(2\pi \left(v_{xLO}x+v_{yLO}y\right)+\phi \left(x,y,\mathrm{e.g}=0\right)\right)\text{sin}\left(\Delta \omega t\right)\end{array}$$

or written differently $$\begin{array}{l}I\left(x,y,t\right)/\left(n_0{c}_0{e}_0\right)\\ ={\mathrm{<figure-callout\; id="0"\; label="E\; L"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_L^0+2\left(E_{\mathrm{right}tOt}\left(x,y,\mathrm{e.g}=0\right)\text{cos}\left(\Delta \omega t\right)+E_{itOt}\left(x,y,\mathrm{e.g}=0\right)\text{sin}\left(\Delta \omega t\right)\right).\end{array}$$

wobei q die Elektronenladung und ℏω die Photonenenergie bezeichnen, η₀ die statische und η₁ dynamische Quantenausbeute bedeuten und angenommen wurde, dass im pmd-Detektor jeder Pixel mit der Frequenz Δv moduliert wird.Through the detection process, the complex amplitude distribution of the light wave E ₀ (x,y,z = 0) exp(-iφ(x,y,z = 0)) is “mixed down” into the complex spatial distribution of the high-frequency signal and can thus be completely, i.e can be determined according to amount and phase for each point in the sensor plane (x,yz=0). For small difference frequencies Δv < 20 Hz, the alternating component can be evaluated directly with a video measuring camera. It should be noted that the interference pattern to be recorded does not change during the exposure time of at least one period T = 1/Δv. Significantly higher differential frequencies, preferably around Δv˜100 MHz, are consequently required for recording moving objects, as are offered in particular by synchronously time-integrating active pixels pmd CMOS sensors. These sensors use a spatiotemporal modulation of the generated photoelectrons and provide for each pixel a time-dependent characteristic of photocurrent iph (x,y,t) and incident light power P(x,y,t) = AI{x,y on a pixel of area A , t) of the form $$i_{pH}\left(x,y,t\right)=\left(\frac{q{n}_0}{\hslash \omega }+\frac{q{n}_1}{\hslash \omega }\text{cos}\left(2\pi \Delta vt\right)\right)P\left(x,y,t\right),$$

where q denotes the electron charge and ℏω the photon energy, η ₀ denotes the static and η ₁ the dynamic quantum yield and it was assumed that in the pmd detector each pixel is modulated with the frequency Δv.

Note: The same transfer function can be realized with a classic active pixel CMOS image sensor with an upstream electro-absorption modulator!

ergibt nach (10) bei Modulation des pmd-Detektors mit cos(Δωt) für die Inphase-Komponente $$\begin{array}{l}<i_{phi}\left(x,y,t\right)>=\left(n_0{c}_0{\epsilon }_0\right)\\ \left(\frac{q{\eta }_0}{\hslash \omega }{E}_{LO}^2+\frac{q{\eta }_1}{\hslash \omega }{E}_{LO}{E}_0\left(x,y,z=0\right)\text{cos}\left(2\pi \left({\nu }_{xLO}x+{\nu }_{yLO}y\right)+\phi \left(x,y,z=0\right)\right)\right)\end{array}$$

und entsprechend erhält man bei Modulation des Detektors mit sin(Δωt) die Quadraturkomponente. $$\begin{array}{l}<i_{phq}\left(x,y,t\right)>=\left(n_0{c}_0{\epsilon }_0\right)\\ \left(\frac{q{\eta }_0}{\hslash \omega }{E}_{LO}^2+\frac{q{\eta }_1}{\hslash \omega }{E}_{LO}{E}_0\left(x,y,z=0\right)\text{sin}\left(2\pi \left({\nu }_{xLO}x+{\nu }_{yLO}y\right)+\phi \left(x,y,z=0\right)\right)\right)\end{array}$$

Temporal averaging over m periods of the high-frequency signal according to $$<i_{pH}\left(x,y,t\right)>=\left(\frac{1}{mT}\right){\displaystyle {\int }_0^{mT}{i}_{pH}\left(x,y,t\right)\mathrm{i.e}t}$$

results from (10) with modulation of the pmd detector with cos(Δωt) for the in-phase component $$\begin{array}{l}<i_{pHi}\left(x,y,t\right)>=\left(n_0{c}_0{e}_0\right)\\ \left(\frac{\mathrm{<figure-callout\; id="0"\; label="q\; n"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">q</figure-callout>}{n}_{}{}_0}{\hslash \omega }{\mathrm{<figure-callout\; id="2"\; label="E\; L\; O"\; filenames="DE102021132521A1\_0061.png,DE102021132521A1\_0062.png"\; state="\{\{state\}\}">E</figure-callout>}}_{LO}^{}+\frac{\mathrm{<figure-callout\; id="1"\; label="q\; n"\; filenames="DE102021132521A1\_0058.png,DE102021132521A1\_0061.png"\; state="\{\{state\}\}">q</figure-callout>}{n}_{}{}_1}{\hslash \omega }{E}_{LO}{E}_0\left(x,y,\mathrm{e.g}=0\right)\text{cos}\left(2\pi \left(v_{xLO}x+v_{yLO}y\right)+\phi \left(x,y,\mathrm{e.g}=0\right)\right)\right)\end{array}$$

and correspondingly, when the detector is modulated with sin(Δωt), the quadrature component is obtained. $$\begin{array}{l}<i_{pHq}\left(x,y,t\right)>=\left(n_0{c}_0{e}_0\right)\\ \left(\frac{\mathrm{<figure-callout\; id="0"\; label="q\; n"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">q</figure-callout>}{n}_{}{}_0}{\hslash \omega }{\mathrm{<figure-callout\; id="2"\; label="E\; L\; O"\; filenames="DE102021132521A1\_0061.png,DE102021132521A1\_0062.png"\; state="\{\{state\}\}">E</figure-callout>}}_{LO}^{}+\frac{\mathrm{<figure-callout\; id="1"\; label="q\; n"\; filenames="DE102021132521A1\_0058.png,DE102021132521A1\_0061.png"\; state="\{\{state\}\}">q</figure-callout>}{n}_{}{}_1}{\hslash \omega }{E}_{LO}{E}_0\left(x,y,\mathrm{e.g}=0\right)\text{sin}\left(2\pi \left(v_{xLO}x+v_{yLO}y\right)+\phi \left(x,y,\mathrm{e.g}=0\right)\right)\right)\end{array}$$

Without object light, the signal is simple: $$<i_{pH0}\left(x,y,t\right)>=\left(n_0{c}_0{e}_0\right)\left(\frac{\mathrm{<figure-callout\; id="0"\; label="q\; n"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">q</figure-callout>}{n}_{}{}_0}{\hslash \omega }{E}_{LO}^2\right).$$

It is interesting that apparently a low dynamic quantum efficiency η ₁ can be compensated by a strong local oscillator field E _LO .

With a constant field strength of the object wave, the differential measurement signal increases proportionally with the square root of the local oscillator intensity $$<i_{pHi,q}\left(x,y,t\right)>-<i_{pH0}\left(x,y,t\right)>\propto E_{LO}.$$

und entsprechend $$E_{itot}\left(x,y,z=0\right)=\left(<i_{phq}\left(x,y,t\right)>-<i_{ph0}\left(x,y,t\right)>\right)\hslash \omega /\left(n_0{c}_0{\epsilon }_{0}q{\eta }_1{E}_{LO}\right).$$

Taking (7) and (8) into account, it can be seen 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, because it is valid $$E_{\mathrm{right}tOt}\left(x,y,\mathrm{e.g}=0\right)=\left(<i_{pHi}\left(x,y,t\right)>-<i_{pH0}\left(x,y,t\right)>\right)\hslash \omega /\left(n_0{c}_0{e}_{0}q{n}_0{E}_{LO}\right)$$

and accordingly $$E_{itOt}\left(x,y,\mathrm{e.g}=0\right)=\left(<i_{pHq}\left(x,y,t\right)>-<i_{pH0}\left(x,y,t\right)>\right)\hslash \omega /\left(n_0{c}_0{e}_{0}q{n}_1{E}_{LO}\right).$$

ein zweidimensionales analytisches Signal, analog zu einem eindimensionalen Signal mit einseitigem Spektrum. Der Realteilteil des Überlagerungsfeldes (19) bestimmt nach (13) und (16) die Ortsabhängigkeit des Messignals. Es gilt $$\begin{array}{l}2Re\left\{E_S\left(x,y,z=0\right)\right\}=2\left\{E_0\left(x,y,z=0\right)\text{cos}\left(2\pi \left({\nu }_{xLO}x+{\nu }_{yLO}y\right)+\phi \left(x,y,z=0\right)\right)\right\}\\ =\text{exp}\left(2\pi i\left({\nu }_{xLO}x+{\nu }_{yLO}y\right)\right)E_0\left(x,y,z=0\right)\text{exp}\left(i\phi \left(x,y,z=0\right)\right)\\ +\text{exp}\left(-2\pi i\left({\nu }_{xLO}x+{\nu }_{yLO}y\right)\right)E_0\left(x,y,z=0\right)\text{exp}\left(-i\phi \left(x,y,z=0\right)\right)\end{array}$$

und die zweidimensionale Fourier-Transformierte ist $$\begin{array}{l}\mathcal{F}\left\{Re\left\{E_S\left(x,y,z=0\right)\right\}\right\}\left({\nu }_x,{\nu }_y\right)\\ =\mathrm{\delta }(\left({\nu }_x-{\nu }_{xLO},{\nu }_y-{\nu }_{yLO}\right)\ast \mathcal{F}\left\{E_0\left(x,y,z=0\right)\text{exp}\left(i\phi \left(x,y,z=0\right)\right)\right\}/2\\ +\mathrm{\delta }(\left({\nu }_x+{\nu }_{xLO},{\nu }_y+{\nu }_{yLO}\right)\ast \mathcal{F}\left\{E_0\left(x,y,z=0\right)\text{exp}\left(-i\phi \left(x,y,z=0\right)\right)\right\}/2,\end{array}$$

wobei * die zweidimensionale Faltung und δ die zweidimensionale δ-Funktion bezeichnen. Die Funktion (21) ist wegen der Bedingung (1) und der Verschiebungseigenschaft der δ-Funktion ist der erste Term auf der rechten Seite der Gleichung (21) nur im ersten Quadranten (v_x > 0,v_y > 0) der (v_x,v_y)-Ebene von Null verschieden und das selbe gilt im vierten Quadranten (v_x < 0,v_y < 0) für den zweiten Term der rechten Seite von (21) verschieden. Mit der Signum-Funktion $$sgn\left({\nu }_x\right)=\{\begin{array}{r}\hfill +1f\ddot{u}r{\nu }_x>0\\ \hfill 0f\ddot{u}r{\nu }_x=0\\ \hfill -1f\ddot{u}r{\nu }_x<0\end{array}$$

ergibt sich damit die interessante Beziehung $$\begin{array}{l}\left(1+sgn\left({\nu }_x\right)\right)\left(1+sgn\left({\nu }_y\right)\right)\mathcal{F}\left\{Re\left\{E_S\left(x,y,z=0\right)\right\}\right\}\left({\nu }_x,{\nu }_y\right)\\ =2\mathrm{\delta }(\left({\nu }_x-{\nu }_{xLO},{\nu }_y-{\nu }_{yLO}\right)\ast \mathcal{F}\left\{E_0\left(x,y,z=0\right)\text{exp}\left(i\phi \left(x,y,z=0\right)\right)\right\}.\end{array}$$

Inverse Fourier-Transformation liefert (entsprechend (20)) $$\begin{array}{l}{\mathcal{F}}^{-\text{i}}\left\{\left(1+sgn\left({\nu }_x\right)\right)+\left(1+sgn\left({\nu }_y\right)\right)\mathcal{F}\left\{Re\left\{E_S\left(x,y,z=0\right)\right\}\right\}\left({\nu }_x,{\nu }_y\right)\right\}\left(x,y,z=0\right)\\ =\text{exp}\left(2\pi i\left({\nu }_{xLO}x+{\nu }_{yLO}y\right)\right)E_0\left(x,y,z=0\right)\text{exp}\left(i\phi \left(x,y,z=0\right)\right),\end{array}$$

womit sich die komplexe elektrische Feldverteilung in der Sensorebene unter Berücksichtigung von (20) aus gemessenen Fotostromsignalen und den aus der Aufnahmegeometrie bekannten Raumfrequenzen (v_xLO ,v_yLO) bestimmen lässt gemäß (Kontrolliere Faktor 2!) $$\begin{array}{l}{E}_0\left(x,y,z=0\right)\text{exp}\left(i\phi \left(x,y,z=0\right)\right)=\text{exp}\left(-2\pi i\left({\nu }_{xLO}x+{\nu }_{yLO}y\right)\right)\\ {\mathcal{F}}^{-\text{i}}\left\{\left(1+sgn\left({\nu }_x\right)\right)\left(1+sgn\left({\nu }_y\right)\right)\mathcal{F}\left\{Re\left\{E_S\left(x,y,z=0\right)\right\}\right\}\left({\nu }_x,{\nu }_y\right)\right\}\left(x,y,z=0\right).\end{array}$$

In the case of stationary wave fields, the real and imaginary parts of the complex electric field strength can be measured in two consecutive steps. If the conditions change dynamically, for example due to the movement of the object, the use of beam splitters to generate replicas of object and reference fields can help. When splitting the beam, however, angle-dependent distortions have to be accepted, which can be corrected, but require considerable additional material effort in the detection process and ultimately make the method not particularly attractive for practical applications. Therefore, the following shows how the complex electric field strength of the object light in the sensor plane E ₀ (x,y,z = 0) exp(-iφ(x,y,z = 0)) can be determined by measuring the in-phase component alone according to equation (17) (or alternatively from the quadrature component (18)). The method uses properties of two-dimensional analytical signals. In general, the (v _x ,v _y ) spatial frequency spectrum of the object light at the location of the sensor in the z=0 plane is band-limited according to relation (1), because all waves emanating from a coherently illuminated object arrive at a finite angle of incidence that is significantly smaller than 90° ° to the finitely large area of the sensor. Mixing with a plane reference wave with an even greater angle of incidence, i.e. greater spatial frequency (y _xLO ,v _yLO ), ensures that only frequency components from the first quadrant (v _xLO > 0,v _yLO > 0) differ from zero in the spatial frequency spectrum of the local signal are. This is the complex electric superposition field $$E_S\left(x,y,\mathrm{e.g}=0\right)=E_0\left(x,y,\mathrm{e.g}=0\right)\text{ex}\left(-2\pi i\left(v_{xLO}x+v_{yLO}y\right)-i\phi \left(x,y,\mathrm{e.g}=0\right)\right)$$

a two-dimensional analytical signal, analogous to a one-dimensional signal with a one-sided spectrum. According to (13) and (16), the real part of the superposition field (19) determines the spatial dependence of the measurement signal. It applies $$\begin{array}{l}2Re\left\{E_S\left(x,y,\mathrm{e.g}=0\right)\right\}=2\left\{E_0\left(x,y,\mathrm{e.g}=0\right)\text{cos}\left(2\pi \left(v_{xLO}x+v_{yLO}y\right)+\phi \left(x,y,\mathrm{e.g}=0\right)\right)\right\}\\ =\text{ex}\left(2\pi i\left(v_{xLO}x+v_{yLO}y\right)\right)E_0\left(x,y,\mathrm{e.g}=0\right)\text{ex}\left(i\phi \left(x,y,\mathrm{e.g}=0\right)\right)\\ +\text{ex}\left(-2\pi i\left(v_{xLO}x+v_{yLO}y\right)\right)E_0\left(x,y,\mathrm{e.g}=0\right)\text{ex}\left(-i\phi \left(x,y,\mathrm{e.g}=0\right)\right)\end{array}$$

and is the two-dimensional Fourier transform $$\begin{array}{l}\mathcal{f}\left\{Re\left\{E_S\left(x,y,\mathrm{e.g}=0\right)\right\}\right\}\left(v_x,v_y\right)\\ =\mathrm{\delta }(\left(v_x-v_{xLO},v_y-v_{yLO}\right)\ast \mathcal{f}\left\{E_0\left(x,y,\mathrm{e.g}=0\right)\text{ex}\left(i\phi \left(x,y,\mathrm{e.g}=0\right)\right)\right\}/2\\ +\mathrm{\delta }(\left(v_x+v_{xLO},v_y+v_{yLO}\right)\ast \mathcal{f}\left\{E_0\left(x,y,\mathrm{e.g}=0\right)\text{ex}\left(-i\phi \left(x,y,\mathrm{e.g}=0\right)\right)\right\}/2,\end{array}$$

where * denotes the two-dimensional convolution and δ denotes the two-dimensional δ-function. The function (21) is, because of the condition (1) and the shifting property of the δ-function, the first term on the right-hand side of the equation (21) is only in the first quadrant (v _x > 0,v _y > 0) of the (v _x ,v _y )-plane is non-zero and the same is different in the fourth quadrant (v _x < 0,v _y < 0) for the second term of the right-hand side of (21). With the Signum function $$sGn\left(v_x\right)=\{\begin{array}{r}\hfill +1f\ddot{\mathrm{and}}\mathrm{right}{v}_x>0\\ \hfill 0f\ddot{\mathrm{and}}\mathrm{right}{v}_x=0\\ \hfill -1f\ddot{\mathrm{and}}\mathrm{right}{v}_x<0\end{array}$$

this leads to the interesting relationship $$\begin{array}{l}\left(1+sGn\left(v_x\right)\right)\left(1+sGn\left(v_y\right)\right)\mathcal{f}\left\{Re\left\{E_S\left(x,y,\mathrm{e.g}=0\right)\right\}\right\}\left(v_x,v_y\right)\\ =2\mathrm{\delta }(\left(v_x-v_{xLO},v_y-v_{yLO}\right)\ast \mathcal{f}\left\{E_0\left(x,y,\mathrm{e.g}=0\right)\text{ex}\left(i\phi \left(x,y,\mathrm{e.g}=0\right)\right)\right\}.\end{array}$$

Inverse Fourier transform yields (according to (20)) $$\begin{array}{l}{\mathcal{f}}^{-\text{i}}\left\{\left(1+sGn\left(v_x\right)\right)+\left(1+sGn\left(v_y\right)\right)\mathcal{f}\left\{Re\left\{E_S\left(x,y,\mathrm{e.g}=0\right)\right\}\right\}\left(v_x,v_y\right)\right\}\left(x,y,\mathrm{e.g}=0\right)\\ =\text{ex}\left(2\pi i\left(v_{xLO}x+v_{yLO}y\right)\right)E_0\left(x,y,\mathrm{e.g}=0\right)\text{ex}\left(i\phi \left(x,y,\mathrm{e.g}=0\right)\right),\end{array}$$

with which the complex electric field distribution in the sensor plane can be determined taking into account (20) from measured photocurrent signals and the spatial frequencies (v _xLO ,v _yLO ) known from the recording geometry according to (check factor 2!) $$\begin{array}{l}{E}_0\left(x,y,\mathrm{e.g}=0\right)\text{ex}\left(i\phi \left(x,y,\mathrm{e.g}=0\right)\right)=\text{ex}\left(-2\pi i\left(v_{xLO}x+v_{yLO}y\right)\right)\\ {\mathcal{f}}^{-\text{i}}\left\{\left(1+sGn\left(v_x\right)\right)\left(1+sGn\left(v_y\right)\right)\mathcal{f}\left\{Re\left\{E_S\left(x,y,\mathrm{e.g}=0\right)\right\}\right\}\left(v_x,v_y\right)\right\}\left(x,y,\mathrm{e.g}=0\right).\end{array}$$

In 2 Various spectra are shown schematically to illustrate the considerations described in equations (19) to (24) for determining the complex, location-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. The determination of the real part of the location-dependent field strength is a special feature, not only because it allows measurements up to the quantum noise limit in practice, but also because it allows short-term or high-frequency measurements up to almost the single-digit nanosecond range or gigahertz range in an excellent way and is therefore more moving for registration objects is well suited. In simple variants of the method, spatially resolved depth determinations in the z-direction, ie in the viewing direction, are possible, for example using holographic two-wavelength methods or speed measurements in the z-direction by utilizing the Doppler effect.

wobei k = 2π/λ = ω/c₀ die Vakuumwellenzahl ist. Eine Sammellinse mit Brechungsindex n₀, Dicke Δz , Brennweite f in der Sensorebene z = 0 resultiert in einer zusätzlichen quadratischen Phasendrehung mit dem Amplitudentransmissionsfaktor $$t\left(x,y\right)=\text{exp}\left[ik\left(n_0-1\right)\Delta z\right]\text{exp}\left(-\frac{ik}{2ƒ}\left[x^2+y^2\right]\right),$$

wobei der erste Faktor eine zusätzliche konstante Phasenverschiebung auf der optischen Achse berücksichtigt. Die elektrische Feldstärkeverteilung in der hinteren Brennebene der Linse, also für z₀ = ƒ ist damit $$\begin{array}{l}E\left(x_0,y_0,z=f\right)=\left(\frac{exp\left(ikƒ\right)}{i\lambda ƒ}\right)exp\left[ik\left(n_0-1\right)\Delta z\right]exp\left(-\frac{ik}{2ƒ}\left[x_0{}^2+y_0{}^2\right]\right)\\ {\displaystyle \int {\displaystyle {\int }_{-\infty }^{\infty }\text{E}\left(\text{x},\text{y},\text{z}=0\right)\text{exp}\left(-i\frac{2\pi }{\lambda ƒ}\left[x{x}_0+y{y}_0\right]\right)dxdy.}}\end{array}$$

The complex electric field strength profile E(x,y,z=0) measured with the pmd sensor in the plane z = 0 is related to the field strength distribution E(x,y,z=z ₀ ) in the plane z = z ₀ > 0 via the diffraction integral. In a paraxial approximation, $$\begin{array}{l}E\left(x,y,\mathrm{e.g}={\mathrm{e.g}}_0\right)=\\ \left(\frac{exp\left(ik{\mathrm{e.g}}_0\right)}{i{\mathrm{e.g}}_0\lambda }\right){\displaystyle \int {\displaystyle {\int }_{-\infty }^{\infty }E\left(x,y,\mathrm{e.g}=0\right)exp\left(\frac{ik}{2{\mathrm{e.g}}_0}\left[{\left(x_0-x\right)}^2+{\left(y_0-y\right)}^2\right]\right)\mathrm{i.e}x\mathrm{i.e}y}},\end{array}$$

where k = 2π/λ = ω/c ₀ is the vacuum wavenumber. A converging lens with refractive index n ₀ , thickness Δz , focal length f in the sensor plane z = 0 results in an additional quadratic phase rotation with the amplitude transmission factor $$t\left(x,y\right)=\text{ex}\left[ik\left(n_0-1\right)\Delta \mathrm{e.g}\right]\text{ex}\left(-\frac{ik}{2ƒ}\left[x^2+y^2\right]\right),$$

where the first factor takes into account 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 z ₀ = ƒ is thus $$\begin{array}{l}E\left(x_0,{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">y</figure-callout>}}_0,\mathrm{e.g}=f\right)=\left(\frac{exp\left(ikƒ\right)}{i\lambda ƒ}\right)exp\left[ik\left({\mathrm{<figure-callout\; id="0"\; label="n"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">n</figure-callout>}}_0-1\right)\Delta \mathrm{e.g}\right]exp\left(-\frac{i\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="DE102021132521A1\_0061.png,DE102021132521A1\_0062.png"\; state="\{\{state\}\}">k</figure-callout>}}{2ƒ}\left[x_0{}^2+{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">y</figure-callout>}}_0{}^2\right]\right)\\ {\displaystyle \int {\displaystyle {\int }_{-\infty }^{\infty }\text{E}\left(\text{x},\text{y},\text{e.g}=0\right)\text{ex}\left(-i\frac{2\pi }{\lambda ƒ}\left[x{x}_0+y{y}_0\right]\right)\mathrm{i.e}x\mathrm{i.e}y.}}\end{array}$$

Except for the constant factor 1/(iλf) and a phase factor that is only dependent on the coordinates (x ₀ ,y ₀ ), this is 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 appropriate $$\begin{array}{l}\text{I}\left(x_0,{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">y</figure-callout>}}_0,\text{e.g}=\text{f}\right)={\left|\text{E}\left(x_0,{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">y</figure-callout>}}_0,\text{e.g}=\text{f}\right)\right|}^2\\ =1/{\left(\lambda ƒ\right)}^2{\left|{\displaystyle \int {\displaystyle {\int }_{-\infty }^{\infty }\text{E}\left(\text{x},\text{y},\text{e.g}=0\right)\text{ex}\left(-i\frac{2\pi }{\lambda ƒ}\left[x{x}_0+y{y}_0\right]\right)\mathrm{i.e}x\mathrm{i.e}y}}\right|}^2.\end{array}$$

The calculation of the intensity distribution in other planes can be done 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, with which the object can be reconstructed in its entire depth.

zu fordern. Bei Differenzfrequenzen von Δv ≈ 100 MHz lassen sich Integrationszeiten von mT = m/ Δv ≈ 100 ns realisieren. Damit gilt für maximal zulässige Geschwindigkeiten in z-Richtung $v_{z}mT\ll \lambda \text{oder}\left(\text{mit}\mathrm{\lambda }=1\mathrm{\mu }\text{m},\text{m}=10\right)v_z\ll 10m/s=36km/Std.$

The coherent recording of optical interference fields usually requires that the object and the recording system do not move. More specifically, the interference pattern to be recorded should not smudge during exposure. There are displacements in the direction of the optical axis, in this case in the z-direction $\mathrm{\Delta }\text{e.g}\ll \mathrm{\lambda }$

to promote. With difference frequencies of Δv ≈ 100 MHz, integration times of mT = m/ Δv ≈ 100 ns can be achieved. This applies to the maximum permissible speeds in the z-direction $v_{\mathrm{e.g}}mT\ll \lambda \text{or}\left(\text{With}\mathrm{\lambda }=1\mathrm{\mu }\text{m},\text{m}=10\right)v_{\mathrm{e.g}}\ll 10m/s=36km/St\mathrm{i.e}.$

On the other hand, movements in parts of the object with velocities of v _z = 10 m/s lead to Doppler frequency shifts of δv = vv _z /c ₀ = 10 MHz. Such axial velocities can be detected with detector systems tuned to modified differential frequencies (Δv + δv).

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 that fall on the sensor at the greatest angle Δθ, measured to the optical z-axis. The superposition of these waves with the strong axial local oscillator wave produces patterns of period Δx = λ/sin Δθ.

The considerations presented show that systems for coherent image acquisition can already offer an interesting alternative for one-dimensional fields of application with almost punctiform or only weakly divergent object illumination. The systems are characterized by the highest reception sensitivity, which reaches up to the quantum noise limit. The object is illuminated with the lowest intensity and enables the lowest possible energy consumption. This goes hand in hand with maximum eye safety. In addition to the detection of three-dimensional location coordinates (detection of z-coordinates not yet discussed here!), axial speeds can be detected directly depending on the location.

The analyzes carried out for the near infrared range can be fully transferred to the visible spectral range. In all the areas mentioned there are diode laser systems with a high electrical-optical conversion efficiency of more than 30% and a high coherence length of well over 100 m short optical pulses and pulse trains with minimum pulse lengths of 5 ns can be used.

und setzen noch v_yLO1 = V_yLO2 = 0 und v_xLO1 = v_xLO2 = V_XLO. Der Einfachheit halber betrachten wir ein unmittelbar um die z-Achse im Fernfeld bei $z\approx -z_0/\mathrm{2,}\left|z_0\right|\gg \mathrm{\lambda }$

konzentriertes Objekt, von dem nach eine rückgestreute paraxiale Welle ausgeht, die in der Nähe des Sensors bei z=0 als ebene Welle $$E\left(x,y,z,t\right)=\left|E_0\right|\text{exp}\left(-i{k}_{z1}\left(z-z_0\right)+i{\omega }_{1}t\right)+\left|E_0\right|\text{exp}\left(-i{k}_{z2}\left(z-z_0\right)+i{\omega }_{2}t\right)$$

approximiert werden kann und z₀ den Umweg berücksichtigt, den das Licht zur Beleuchtung des Objekts zusätzlich zurückzulegen hat. Die Sensorabmessungen sind typischerweise klein gegen |z₀| und die Intensität in der Sensorebene z = 0 ist $$\begin{array}{l}I\left(x,y,t\right)=\\ \left\{E_L\left(x,y,z=\mathrm{0,}t\right)+E\left(x,y,z=\mathrm{0,}t\right)\right\}\left\{E_L\left(x,y,z=\mathrm{0,}t\right)\ast +E\left(x,y,z=\mathrm{0,}t\right)\ast \right\},\end{array}$$

wobei der hochgestellte Asterix * die Notation für die Bildung einer konjugiert komplexen Größe bezeichnet. Berechnung mit (21) und (22) ergibt $$\begin{array}{l}I\left(x,y,t\right)=E_{LO}^2\left(2+2\text{cos}\left({\omega }_2-{\omega }_1\right)t\right)\\ +2E_{LO}\left|E_0\right|\left(\text{cos}\left(k_{z1}{z}_0-\Delta \omega t+2\pi {\nu }_{xLO}x\right)+\text{cos}\left(k_{z1}{z}_0+\left({\omega }_1-{\omega }_2-\Delta \omega \right)t+2\pi {\nu }_{xLO}x\right)\right)\\ +2E_{LO}\left|E_0\right|\left(\text{cos}\left(k_{z2}{z}_0-\Delta \omega t+2\pi {\nu }_{xLO}x\right)+\text{cos}\left(k_{z2}{z}_0+\left({\omega }_2-{\omega }_1-\Delta \omega \right)t+2\pi {\nu }_{xLO}x\right)\right)\\ +{\left|E_0\right|}^2\left(2+2\text{cos}\left[\left(k_{z2}-k_{z1}\right)z_0+\left({\omega }_2-{\omega }_1\right)t\right]\right).\end{array}$$

The object is illuminated with two spatially coherent light waves with different frequencies ω ₁ and ω ₂ but the same amplitudes E ₁₀ (x, y, z)=|E ₁ (x,y, z, t)| and E ₂ (x,y,z) = |E ₂ (x,y,z,t)| , where the difference frequency (ω ₁ - ω ₂ )/2π ≈ 100 MHz is typically in the high-frequency range. We choose a reference or local oscillator wave running at an angle to the z-axis $$\begin{array}{l}{E}_L\left(x,y,\mathrm{e.g},t\right)=E_{LO}\text{ex}\left(i\left({\mathrm{<figure-callout\; id="1"\; label="\omega "\; filenames="DE102021132521A1\_0058.png,DE102021132521A1\_0061.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_1+\Delta \omega \right)t-2\pi i\left(v_{xLO1}x+v_{yLO1}y\right)-i{k}_{\mathrm{<figure-callout\; id="1"\; label="e.g\; L\; O"\; filenames="DE102021132521A1\_0058.png,DE102021132521A1\_0061.png"\; state="\{\{state\}\}">e.g</figure-callout>}LO1}\mathrm{e.g}\right)\\ +E_{LO}\text{ex}\left(i\left({\mathrm{<figure-callout\; id="2"\; label="\omega "\; filenames="DE102021132521A1\_0061.png,DE102021132521A1\_0062.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_2+\Delta \omega \right)t-2\pi i\left(v_{xLO2}x+v_{yLO2}y\right)-i{k}_{\mathrm{<figure-callout\; id="2"\; label="e.g\; L\; O"\; filenames="DE102021132521A1\_0061.png,DE102021132521A1\_0062.png"\; state="\{\{state\}\}">e.g</figure-callout>}LO2}\mathrm{e.g}\right).\end{array}$$

and set v _yLO1 = V _yLO2 = 0 and v _xLO1 = v _xLO2 = V _XLO . For the sake of simplicity, we consider an immediately around the z-axis in the far field at $\mathrm{e.g}\approx -{\mathrm{e.g}}_0/\mathrm{2,}\left|{\mathrm{e.g}}_0\right|\gg \mathrm{\lambda }$

concentrated object from which to a backscattered paraxial wave emanates near the sensor at z=0 as a plane wave $$E\left(x,y,\mathrm{e.g},t\right)=\left|{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0\right|\text{ex}\left(-i{k}_{\mathrm{e.g}1}\left(\mathrm{e.g}-{\mathrm{e.g}}_0\right)+i{\omega }_{1}t\right)+\left|{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0\right|\text{ex}\left(-i{k}_{\mathrm{e.g}2}\left(\mathrm{e.g}-{\mathrm{e.g}}_0\right)+i{\omega }_{2}t\right)$$

can be approximated and z ₀ takes into account the additional detour that the light has to travel to illuminate the object. The sensor dimensions are typically small compared to |z ₀ | and the intensity in the sensor plane is z=0 $$\begin{array}{l}I\left(x,y,t\right)=\\ \left\{E_L\left(x,y,\mathrm{e.g}=\mathrm{0,}t\right)+E\left(x,y,\mathrm{e.g}=\mathrm{0,}t\right)\right\}\left\{E_L\left(x,y,\mathrm{e.g}=\mathrm{0,}t\right)\ast +E\left(x,y,\mathrm{e.g}=\mathrm{0,}t\right)\ast \right\},\end{array}$$

where the superscript asterix * denotes the notation for the formation of a conjugate complex quantity. Calculation with (21) and (22) results $$\begin{array}{l}I\left(x,y,t\right)=E_{LO}^2\left(2+2\text{cos}\left({\mathrm{<figure-callout\; id="2"\; label="\omega "\; filenames="DE102021132521A1\_0061.png,DE102021132521A1\_0062.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_2-{\omega }_1\right)t\right)\\ +2E_{LO}\left|{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0\right|\left(\text{cos}\left(k_{\mathrm{e.g}1}{\mathrm{e.g}}_0-\Delta \omega t+2\pi v_{xLO}x\right)+\text{cos}\left(k_{\mathrm{e.g}1}{\mathrm{e.g}}_0+\left({\mathrm{<figure-callout\; id="1"\; label="\omega "\; filenames="DE102021132521A1\_0058.png,DE102021132521A1\_0061.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_1-{\mathrm{<figure-callout\; id="2"\; label="\omega "\; filenames="DE102021132521A1\_0061.png,DE102021132521A1\_0062.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_2-\Delta \omega \right)t+2\pi v_{xLO}x\right)\right)\\ +2E_{LO}\left|{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0\right|\left(\text{cos}\left(k_{\mathrm{e.g}2}{\mathrm{e.g}}_0-\Delta \omega t+2\pi v_{xLO}x\right)+\text{cos}\left(k_{\mathrm{e.g}2}{\mathrm{e.g}}_0+\left({\mathrm{<figure-callout\; id="2"\; label="\omega "\; filenames="DE102021132521A1\_0061.png,DE102021132521A1\_0062.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_2-{\mathrm{<figure-callout\; id="1"\; label="\omega "\; filenames="DE102021132521A1\_0058.png,DE102021132521A1\_0061.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_1-\Delta \omega \right)t+2\pi v_{xLO}x\right)\right)\\ +{\left|{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0\right|}^2\left(2+2\text{cos}\left[\left(k_{\mathrm{e.g}2}-k_{\mathrm{e.g}1}\right){\mathrm{e.g}}_0+\left({\mathrm{<figure-callout\; id="2"\; label="\omega "\; filenames="DE102021132521A1\_0061.png,DE102021132521A1\_0062.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_2-{\omega }_1\right)t\right]\right).\end{array}$$

At the angular frequency Δω is the signal $$\begin{array}{l}{E}_{\Delta \omega }\left(t\right)=2E_{LO}\left|{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0\right|\left[\text{cos}\left(k_{\mathrm{e.g}1}{\mathrm{e.g}}_0-\Delta \omega t+2\pi v_{xLO}x\right)+\text{cos}\left(k_{\mathrm{e.g}2}{\mathrm{e.g}}_0-\Delta \omega t+2\pi v_{xLO}x\right)\right]\\ =2E_{LO}\left|{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0\right|\left[\text{cos}\left(k_{\mathrm{e.g}1}{\mathrm{e.g}}_0+2\pi v_{xLO}x\right)\text{cos}\Delta \omega t+\text{sin}\left(k_{\mathrm{e.g}2}{\mathrm{e.g}}_0+2\pi v_{xLO}x\right)\text{sin}\Delta \omega t\right]\\ +2E_{LO}\left|{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0\right|\left[\text{cos}\left(k_{\mathrm{e.g}2}{\mathrm{e.g}}_0+2\pi v_{xLO}x\right)\text{cos}\Delta \omega t+\text{sin}\left(k_{\mathrm{e.g}2}{\mathrm{e.g}}_0+2\pi v_{xLO}x\right)\text{sin}\Delta \omega t\right].\end{array}$$

wobei c₀ die Lichtgeschwindigkeit im Vakuum bezeichnet. Auf dem synchronen Sensor ergibt sich gemäß der Kennlinie (11) auf dem ganz wesentlich durch die starke Referenzwelle bestimmte gleichmäßige Untergrundintensität ein Cosinusförmig moduliertes Streifenmuster, genauer gesagt ein Schwebungssignal in x-Richtung, dessen Periode 1/v_xLO von der Raumfrequenz der Referenzwelle abhängt und dessen Amplitude sich mit der Tiefenkoordinate z₀ des Objekts periodisch ändert. Demgemäß erhält man nach (13) für die Inphase-Komponente des gemessenen Fotostroms die Beziehung $$\begin{array}{l}<i_{phi}\left(x,y,t\right)>=<i_{phi}\left(x\right)>=\left(n_0{c}_0{\epsilon }_0\right)\left(\frac{q{\eta }_0}{\hslash \omega }2E_{LO}^2\right)\\ +\left(\frac{q{\eta }_1}{\hslash \omega }2E_{LO}\left|E_0\right|\text{cos}\left(k_{z2}-k_{z1}\right)z_0/2)\text{cos}\left[2\pi {\nu }_{xLO}x+\left(k_{z2}+k_{z1}\right)z_0/2)\right]\right).\end{array}$$

Cross-correlation, ie multiplication by cos Δωt and time integration over an integer m of periods T=1/Δω, provides the signal $$\begin{array}{l}\left(\frac{1}{mT}\right){\displaystyle {\int }_0^{mT}{E}_{\Delta \omega }\left(t\right)\text{cos}\Delta \omega t}\mathrm{i.e}t\\ =2E_{LO}\left|E_0\right|\text{cos}\left[\left(k_{\mathrm{e.g}2}-k_{\mathrm{e.g}1}\right){\mathrm{e.g}}_0/2\right]\text{cos}\left[2\pi v_{xLO}x+\left(k_{\mathrm{e.g}2}+k_{\mathrm{e.g}1}\right){\mathrm{e.g}}_0/2)\right]\\ \approx 2E_{LO}\left|E_0\right|\text{cos}\left[\left({\omega }_2-{\omega }_1\right){\mathrm{e.g}}_0/2c_0\right]\text{cos}\left[2\pi v_{xLO}x+{\omega }_1{\mathrm{e.g}}_0/2c_0\right],\end{array}$$

where c ₀ denotes the speed of light in a vacuum. On the synchronous sensor, according to the characteristic curve (11), a cosine-shaped modulated fringe pattern results, more precisely a beat signal in the x-direction, whose period 1/v _xLO depends on the spatial frequency of the reference wave and whose amplitude changes periodically with the depth coordinate z ₀ of the object. Accordingly, according to (13) one obtains the relation for the in-phase component of the measured photocurrent $$\begin{array}{l}<i_{pHi}\left(x,y,t\right)>=<i_{pHi}\left(x\right)>=\left(n_0{c}_0{e}_0\right)\left(\frac{\mathrm{<figure-callout\; id="0"\; label="q\; n"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">q</figure-callout>}{n}_{}{}_0}{\hslash \omega }2E_{LO}^2\right)\\ +\left(\frac{\mathrm{<figure-callout\; id="1"\; label="q\; n"\; filenames="DE102021132521A1\_0058.png,DE102021132521A1\_0061.png"\; state="\{\{state\}\}">q</figure-callout>}{n}_{}{}_1}{\hslash \omega }2E_{LO}\left|{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0\right|\text{cos}\left(k_{\mathrm{e.g}2}-k_{\mathrm{e.g}1}\right){\mathrm{e.g}}_0/2)\text{cos}\left[2\pi v_{xLO}x+\left(k_{\mathrm{e.g}2}+k_{\mathrm{e.g}1}\right){\mathrm{e.g}}_0/2)\right]\right).\end{array}$$

das über die Sensorfläche als zeitlich und räumlich konstant anzusetzen ist. Der Kontrast K des räumlichen Schwebungssignals in x-Richtung ist gegeben durch $$K\left(z_0\right)=\frac{<i_{phi,max}\left(x\right)>-<i_{phi,min}\left(x\right)>}{<i_{phi,max}\left(x\right)>+<i_{phi,min}\left(x\right)>}=\left(\left|E_0\right|/E_{LO}\right)\left|\text{cos}\left(\left(k_{z2}-k_{z1}\right)z_0/2\right)\right|$$

Without object light, the photocurrent signal is only determined by the strong local oscillator light $$<i_{pH0}\left(x,y,t\right)>=\left(n_0{c}_0{e}_0\right)\left(\frac{q{n}_0}{\hslash \omega }2E_{LO}^2\right),$$

which can be assumed to be temporally and spatially constant across the sensor surface. The contrast K of the spatial beat signal in the x-direction is given by $$K\left({\mathrm{e.g}}_0\right)=\frac{<i_{pHi,max}\left(x\right)>-<i_{pHi,min}\left(x\right)>}{<i_{pHi,max}\left(x\right)>+<i_{pHi,min}\left(x\right)>}=\left(\left|{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0\right|/E_{LO}\right)\left|\text{cos}\left(\left(k_{\mathrm{e.g}2}-k_{\mathrm{e.g}1}\right){\mathrm{e.g}}_0/2\right)\right|$$

3 shows a method for determining the depth coordinates of a punctiformly 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 process.

gegeben ist. Auswertung mit der modifizierten Referenzwelle wie in (27) bis (29) liefert der ebenen Referenzwelle (21) überlagert und gleichzeitig mit (26) ausgewertet. Das der Gleichung (26) entsprechende modifizierte Signal ist $$\begin{array}{l}\left(\frac{1}{mT}\right){\displaystyle {\int }_0^{mT}{E}_{\Delta \omega ,mon}\left(t\right)\text{cos}\Delta \omega t}dt\\ =E_{LO}\left|E_0\right|\text{cos}\left[2\pi {\nu }_{xLO}x+k_{z1}{z}_0\right]=E_{LO}\left|E_0\right|\text{cos}\left[2\pi {\nu }_{xLO}x+{\omega }_1{z}_0/2c_0\right].\end{array}$$

Contrast can be used to precisely determine z ₀ if, as in shown schematically proceeds. The bichromatic light backscattered from the object is superimposed on a partial area of the sensor with the bichromatic reference wave (21) and at the same time on another separate part of the sensor with the monochromatic partial wave of (21), which is caused by $$E_{LmOn}\left(x,y,\mathrm{e.g},t\right)=E_{LO}\text{ex}\left(i\left({\mathrm{<figure-callout\; id="1"\; label="\omega "\; filenames="DE102021132521A1\_0058.png,DE102021132521A1\_0061.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_1+\Delta \omega \right)t-2\pi i\left(v_{xLO1}x+v_{yLO1}y\right)-i{k}_{\mathrm{<figure-callout\; id="1"\; label="e.g\; L\; O"\; filenames="DE102021132521A1\_0058.png,DE102021132521A1\_0061.png"\; state="\{\{state\}\}">e.g</figure-callout>}LO1}\mathrm{e.g}\right)$$

given is. Evaluation with the modified reference wave as in (27) to (29) supplies the plane reference wave (21) superimposed and evaluated at the same time with (26). The modified signal corresponding to equation (26) is $$\begin{array}{l}\left(\frac{1}{mT}\right){\displaystyle {\int }_0^{mT}{E}_{\Delta \omega ,mOn}\left(t\right)\text{cos}\Delta \omega t}\mathrm{i.e}t\\ =E_{LO}\left|{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0\right|\text{cos}\left[2\pi v_{xLO}x+k_{\mathrm{e.g}1}{\mathrm{e.g}}_0\right]=E_{LO}\left|{\mathrm{<figure-callout\; id="0"\; label="E"\; filenames="DE102021132521A1\_0057.png"\; state="\{\{state\}\}">E</figure-callout>}}_0\right|\text{cos}\left[2\pi v_{xLO}x+{\mathrm{<figure-callout\; id="1"\; label="\omega "\; filenames="DE102021132521A1\_0058.png,DE102021132521A1\_0061.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_1{\mathrm{e.g}}_0/2c_0\right].\end{array}$$

und mit dem modifizierten Kontrast K_mon (z₀) = (|E₀ | /E_LO) lässt sich z₀ aus dem Verhältnis $$K\left(z_0\right)/K_{mon}\left(z_0\right)=\left|\text{cos}\left(\left(k_{z2}-k_{z1}\right)z_0/2\right)\right|=\left|\text{cos}\left[\left({\omega }_2-{\omega }_1\right)z_0/2c_0\right]\right|$$

ermitteln. Der Kontrast ändert sich periodisch mit z₀. Die Bedingung für maximalen Kontrast ist z_0,2m = 2mπc₀/(ω₂ - ω₁), wobei m eine ganze Zahl ist. Minimalen Kontrast findet man fürz_0(2m+1) = (2m + 1)πc₀/(ω₂ - ω₁).The same applies to the measured photocurrent signal $$\begin{array}{l}<i_{pHi,mOn}\left(x,y,t\right)>/\left(n_0{c}_0{e}_0\right)\\ =\left(\frac{q{n}_0}{\hslash \omega }2E_{LO}^2\right)+\left(\frac{q{n}_1}{\hslash \omega }2E_{LO}\left|E_0\right|\text{cos}\left[2\pi v_{xLO}x+k_{\mathrm{e.g}1}{\mathrm{e.g}}_0\right]\right),\end{array}$$

and with the modified contrast K _mon (z ₀ ) = (|E ₀ | /E _LO ) z ₀ can be calculated from the ratio $$K\left({\mathrm{e.g}}_0\right)/K_{mOn}\left({\mathrm{e.g}}_0\right)=\left|\text{cos}\left(\left(k_{\mathrm{e.g}2}-k_{\mathrm{e.g}1}\right){\mathrm{e.g}}_0/2\right)\right|=\left|\text{cos}\left[\left({\mathrm{<figure-callout\; id="2"\; label="\omega "\; filenames="DE102021132521A1\_0061.png,DE102021132521A1\_0062.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_2-{\omega }_1\right){\mathrm{e.g}}_0/2c_0\right]\right|$$

determine. The contrast changes periodically with z ₀ . The condition for maximum contrast is z _0.2m = 2mπc ₀ /(ω ₂ - ω ₁ ), where m is an integer. Minimum contrast is found forz _0(2m+1) = (2m + 1)πc ₀ /(ω ₂ - ω ₁ ).

The distance measurement method presented for punctiform object illumination can easily be extended to one-dimensional illumination patterns (stripes, lines) and two-dimensional areal illumination. A spatially resolved distance determination is guaranteed for convex objects as long as the waves hitting the sensor from the object and the planar reference wave fulfill condition (1).

4 shows a structure in which an object wave E _Obj reflected by an object and a frequency-shifted reference wave E _Lo are directed to a sensor and brought to interference there. The sensor is designed as a demodulator, demodulates the interference present at the sensor.

und für die Intensität: $$I\approx \left|E^2\right|=a^2+A^2+Re2aA{e}^{i\phi \left(x,y,z\right)}{e}^{-i\omega t}{e}^{ikr}{e}^{-i\omega t-i\mathrm{\Delta }\omega t}$$

mit A » α $$I\approx A^2+2A\left(x,y\right)cos\left(\mathrm{\Delta }\omega t-\phi \left(x,y\right)-kr\right)$$

As already shown in formula (5), the following applies: $$\begin{array}{l}{\text{E}}_{\text{dead}}={\text{E}}_{\text{object}}+{\text{E}}_{\text{Lo}}\\ E_{tOt}=a{e}^{i\phi \left(x,y,\mathrm{e.g}\right)}{e}^{-i\omega t}+A{e}^{ik\mathrm{right}}{e}^{-i\omega t-i\mathrm{\Delta }\omega t}\end{array}$$

and for the intensity: $$I\approx \left|{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="DE102021132521A1\_0061.png,DE102021132521A1\_0062.png"\; state="\{\{state\}\}">E</figure-callout>}}^2\right|=a^2+A^2+Re2aA{e}^{i\phi \left(x,y,\mathrm{e.g}\right)}{e}^{-i\omega t}{e}^{ik\mathrm{right}}{e}^{-i\omega t-i\mathrm{\Delta }\omega t}$$

with A » α $$I\approx A^2+2A\left(x,y\right)cOs\left(\mathrm{\Delta }\omega t-\phi \left(x,y\right)-k\mathrm{right}\right)$$

In order to determine an object distance, it is provided according to the invention to detect the real part with a sensor which demodulates the signal in time with the beat frequency Δω.

In the example according to 4 a laser emits coherent light with a frequency ω ₁ in the direction of an object. To form a reference wave or frequency ω ₁ ', part of the light emitted by the laser is directed onto an optical modulator, here an acousto-optical modulator AOM, which shifts the incoming laser frequency by a modulation frequency Δω present at the optical modulator $${\mathrm{\omega }}_1\text{'}={\mathrm{\omega }}_1\text{'}+\mathrm{\Delta \omega }$$

The sensor is designed as a synchronous demodulator and preferably works according to a photon mixing principle or PMD principle and has an array of light propagation time pixels that detect the interference of the reference and object waves at the sensor phase-synchronously to the modulation frequency Δω.

Object distances can be determined on the basis of the phase-synchronously determined signals.

The modulation frequency Δω is generated with the aid of a modulator which is designed in such a way that the modulation frequency Δω is made available to the optical modulator and the demodulator in phase synchronism or, if necessary, shifted by a predetermined phase position.

5 shows a variant in which the frequency-shifted light wave is directed onto the object and the unshifted light wave serves as a reference.

6 shows a setup for a bichromatic distance measurement according to FIG 3 . In the example shown, a first coherent light wave is generated with the aid of a laser and a second coherent light wave with a second frequency is additionally generated via a downstream acousto-optical modulator. With the aid of a first modulator, the acousto-optical modulator AOM1 is subjected to a modulation frequency by which the AOM shifts the frequency of part of the incoming light wave. Two light waves with different frequencies, with which an object is illuminated, are then present at the output of the acousto-optical modulator AOM1. The two frequencies advantageously differ by 100 to 1000 MHz, the frequency difference preferably being in a range of 200-400 MHz.

As an alternative to this frequency processing, two lasers with two different frequencies can also be used.

A portion of the light waves emerging after the first acousto-optical modulator is directed to a second acousto-optical modulator AOM 2 which is operated at a second modulation frequency of the modulator 2 . The frequencies of the two light waves entering the AOM2 are shifted by the frequency of the modulation frequency present and form the reference waves ω ₁ ', ω ₂ ', which are directed to the demodulator. The second modulation frequency is advantageously in a range from 1 to 100 MHz and particularly advantageously in a range from 40 to 80 MHz. Depending on the configuration of the demodulator, higher modulation frequencies can also be considered.

An object is illuminated with the other part of the light waves ω ₁ , ω ₂ emerging from the first AOM1, the object waves reflected by the object being directed onto the demodulator in such a way that they interfere with the reference waves there.

The superimposition of the two interference patterns is demodulated with the aid of the demodulator and location information of the object is determined.

7 shows a structure with a first and second panel. For reasons of clarity, the angle α _max is shown only schematically. Aperture 1 and Aperture 2 are used for spatial frequency filtering of the object light hitting the sensor. In practice, the apertures are much closer to the sensor (~1 cm x 1 cm) than shown here.

For the object wave applies: $$2E_{LO}Re\left\{E_0\left(x,y,\mathrm{e.g}=0\right)\text{ex}\left(-2\pi i\left(v_{xLO}x+v_{yLO}y\right)-i\phi \left(x,y,\mathrm{e.g}=0\right)\right)\text{ex}\left(i\Delta \omega t\right)\right\}$$

Or.: $$\begin{array}{l}2E_{LO}{E}_0\left(x,y,\mathrm{e.g}=0\right)\text{cos}\left(2\pi \left(v_{xLO}x+v_{yLO}y\right)+\phi \left(x,y,\mathrm{e.g}=0\right)\right)\text{cos}\left(\Delta \omega t\right)\\ +2E_{LO}{E}_0\left(x,y,\mathrm{e.g}=0\right)\text{sin}\left(2\pi \left(v_{xLO}x+v_{yLO}y\right)+\phi \left(x,y,\mathrm{e.g}=0\right)\right)\text{sin}\left(\Delta \omega t\right)\end{array}$$

The following applies to the reference wave: $$E_{LO}\text{ex}\left(i\left(\omega +\Delta \omega \right)t-2\pi i\left(v_{xLO}x+v_{yLO}y\right)\right)$$

The pmd processor performs a (synchronous) cross-correlation with cos(Δωt) and delivers the location-dependent real measurement signal proportional to: $$E_{LO}{E}_0\left(x,y,\mathrm{e.g}=0\right)\text{cos}\left(2\pi \left(v_{xLO}x+v_{yLO}y\right)+\phi \left(x,y,\mathrm{e.g}=0\right)\right)$$

A second processor calculates the complex amplitude of the electric field strength of the object wave in the sensor plane z = 0 pixel by pixel from the measurement signal: $$E_0\left(x,y,\mathrm{e.g}=0\right)\text{ex}\left(i\phi \left(x,y,\mathrm{e.g}=0\right)\right)$$

Another processor uses the complex amplitude of the electrical field strength of the object light wave in the z = 0 plane to calculate the propagation of the wave into other planes, whereby optical elements such as lenses can also be taken into account.

From this, the following arrangement can be implemented:

1. a) einem Lasersystem, das kurze, typisch Δt ≈ 100 ns lange kohärente Lichtimpulse mit Kreisfrequenz ω und spektraler Bandbreite δω < 2π/ Δt emittiert, vorzugsweise einer kantenemittierenden Laserdiode mit externem Gitterreflektor.
2. b) einem Strahlteiler, der einen ersten Strahl zur Objektbeleuchtung und einen zweiten um Δω > δω frequenzverschobenen zweiten Strahl zur Referenz erzeugt. Der Strahlteiler ist vorzugsweise als akusto-optischer Modulator ausgebildet, der bei der Frequenz Δω ≈ 100 MHz betrieben wird,
3. c) einem ersten Strahlengang bei der Lichtfrequenz ω+ Δω, der als ebene Welle schräg unter dem Winkel αLO, gemessen gegen die optische Achse auf den Sensor fällt.
4. d) einem zweiten Strahlengang zur Beleuchtung eines diffus reflektierenden Objekts bei der Lichtfrequenz ω.
5. e) einem Raumfrequenzfiltersystem, das dafür sorgt, dass vom Objekt rückgestreute Lichtstrahlen mit einem maximalen Winkel amax mit amax < αLO auf den Bildsensor treffen. Das Raumfrequenzfiltersystem wird im einfachsten Fall zweckmäßigerweise durch Blenden realisiert.
6. f) einem flächenhaften Bildsensor, vorzugsweise einem CMOS Bildsensor endlicher Größe, dessen Pixelempfindlichkeit sich synchron mit der Frequenz Δω steuern lässt und dessen räumliche Auflösung hoch genug ist, um das Intensitätsüberlagerungsmuster von Referenz- und Objektlicht naturgetreu aufzeichnen zu können. Vorzugsweise wird für diesen Zweck ein pmd-Bildsensor genutzt.
7. g) einer ersten und zweiten Prozessoreinheit, die aus dem pixelweise gemessenen reellen Messsignal die pixelweise vorliegende ortsabhängige komplexe Amplitude der elektrischen Feldstärke des Objektlichts in der Sensorebene nach Betrag und Phase generiert.
8. h) einer weiteren Prozessoreinheit, die ausgehend von der komplexen Feldverteilung in der Sensorebene die Propagation des Feldes entlang der optischen Achse berechnet. Insbesondere lassen sich damit auch Abbildungen des Objekts berechnen, wenn die Wirkung einer optischen Sammellinse in die Propagation des Feldes numerisch berücksichtigt wird. Sozusagen nachträglich nach Aufnahme des Hologramms und Berechnung der komplexen Feldverteilung der Objektlichtwelle lassen sich damit bei geeigneter Wahl der Bildweite und der Brennweite der numerisch simulierten optischen Linse scharfe Bilder von verschiedenen Tiefenebenen des Objekts erzeugen.

Arrangement for recording short-term holograms of moving objects using heterodyne technology, consisting of

1. a) a laser system that emits short, typically Δt ≈ 100 ns long coherent light pulses with angular frequency ω and spectral bandwidth δω < 2π/ Δt, preferably an edge-emitting laser diode with an external grating reflector.
2. b) a beam splitter, which generates a first beam for object illumination and a second beam, frequency-shifted by Δω > δω, for reference. The beam splitter is preferably designed as an acousto-optical modulator, which is operated at the frequency Δω ≈ 100 MHz,
3. c) a first beam path at the light frequency ω+ Δω, which falls on the sensor as a plane wave at an angle αLO, measured against the optical axis.
4. d) a second beam path for illuminating a diffusely reflecting object at the light frequency ω.
5. e) a spatial frequency filter system that ensures that light rays scattered back from the object hit the image sensor at a maximum angle amax with amax < αLO. In the simplest case, the spatial frequency filter system is expediently implemented by screens.
6. f) an areal image sensor, preferably a CMOS image sensor of finite size, whose pixel sensitivity can be controlled synchronously with the frequency Δω and whose spatial resolution is high enough to be able to record the intensity superimposition pattern of reference and object light faithfully. A pmd image sensor is preferably used for this purpose.
7. g) a first and second processor unit, which generates the pixel-by-pixel location-dependent complex amplitude of the electric field strength of the object light in the sensor plane from the real measurement signal measured pixel-by-pixel according to amount and phase.
8. h) a further processor unit, which calculates the propagation of the field along the optical axis based on the complex field distribution in the sensor plane. In particular, it is also possible to calculate images of the object if the effect of an optical converging lens on the propagation of the field is taken into account numerically. After the recording of the hologram and calculation of the complex field distribution of the object light wave, so to speak, sharp images of different depth levels of the object can be generated with a suitable choice of the image length and the focal length of the numerically simulated optical lens.

In analogy to videos, hologram sequences can be generated from the object by exposure to laser light pulse sequences.

Claims (6)

Arrangement for recording short-term holograms of moving objects using heterodyne technology, consisting of a) a laser system that emits coherent light with a first frequency (ω ₁ ), b) with a beam splitter that splits the coherent light pulse for object illumination and a second one by a difference frequency (Δω > δω) generates a frequency-shifted reference light pulse, c) with a first beam path in which the reference light pulse (ω+ Δω) impinges on a sensor as a plane wave at an angle of incidence (α _LO ), measured against the optical axis, d) with a second beam path for illuminating an object with the coherent light pulse of the first frequency, e) with a spatial frequency filter system which ensures that light rays scattered back from the object hit the image sensor at a maximum angle α _max with α _max <α _LO . arrangement according to claim 1 , in which the light is emitted in light pulses <= 100 ns and/or the image sensor has an integration time <= 100 ns. Arrangement according to one of the preceding claims, in which the beam splitter is designed as an acousto-optical modulator. arrangement according to claim 3 , in which the beam splitter operates at the frequency in the range of 1-100 MHz. Arrangement according to one of the preceding claims, in which the spatial frequency filter system is implemented by at least one diaphragm. Arrangement according to one of the preceding claims, with an oscillator for generating a modulation frequency (Δω), with an optical modulator for generating a reference light wave (E _LO , ω ₁ '), with a PMD sensor with a plurality of 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 or laser system is directed onto the optical modulator and the optical modulator shifts the first frequency (ω ₁ ) of the incoming light by the modulation frequency (Δω), so that a reference light wave (E _LO ) with a second frequency (ω ₁ ') is available at the output of the optical modulator, with 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 (E _Obj ) where the PMD Sensor is illuminated with the object light wave (E _Obj ) and the reference light wave (E _LO ) in such a way that the angles of incidence or the directions of propagation of the two waves are aligned at a predetermined angle (α) to one another and both waves interfere, with the interference changing over time and has a period corresponding to the frequency shift (Δω) or the modulation frequency (Δω), with the interference being detected alternately by the first and second integration nodes (A,B) in phase-synchronous fashion with the modulation frequency (Δω), with 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 angle of incidence of the Object and reference wave, a laterally resolved amplitude and a laterally resolved phase of the object wave can be determined.

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