:

Optical Range-Sensing with spatially modulated Coherence

M. Bail, B. Gebhardt, G. Häusler, J. Herrmann, V. Höfer, M Lindner, P. Pavlicek, R.Ringler

1. Introduction

Chair for Optics, University of Erlangen Staudtstr. 7, 0 91058 Erlangen, Gennany

Optical range sensors utilize different types of optical signals: intensity, amplitude and phase~ polarization~ and colour. It has been shown that the different signals have different properties in tenns of meä.suring uncertainty [1 ,2]. F or example, triangulation sensors are severely affected by speckle . noise, and the range uncertainty scales down inversely to the observation aperture.

This undesired behavior can be overcome by proper selection of the optical signal -dependent on the measuring problem. It tums out that spatial- and I or (partial) temporal incoherence can be extremely helpful for new sensors with unique properties.

Here we will discuss the utilization of spatially modulated coherence, for the acquisition of the topology of an object surface and even of the bulk structure of a scattering medium: "coherence radar" [2] without mechanical depth scan, "coherence radar for pseudo-short pulse to1nography" [3], "optical tomography with the "spectral radar". The term "-radar" will become obvious, because there is an equivalence with time-of-flight methods.

2. Coherence radar without mechanical depth scan

The coherence radar [2] is based on white light interferometry on rough surfaces. Instead of measuring the phase of the reflected wave ( which is arbitrary, for a rough obj ect ! ), we measure the location of the maximum contrast in the spatially modulated coherence tunction. The coherence function is scanned, by moving the reference mirror, or the object, along the

optical axis. The unique features of this principle ( and of some related principles such as 2/....­interferometry) are coaxial illumination and observation (no shading) and a range accuracy that is not limited by the aperture, just by the roughness of the object. The principle can be modified to avoid the mechanical depth scan, by intruduction of a dispersive element into the reference arm [4]. The spectrum I(k) of the interferometer output (I= intensity, k=wave

number) is essentially given by

I (k) = l + cos [ 2 a d (k2 - k k0 )] (l)

with, a=dispersion constant, d=thickness of dispersive element, k0 =wavenumber for equal

path length of reference- and object path. Figures 1,2 display the sensor, and the spectrun1 for different object distance. Note that there is no ambiguity in the localisation of the spectrum. It is not anymore periodic, but a ~'chirp", and can be localized with correlation techniques, to achieve a range uncertainty of about 1 micrometer, for rough objects.

Fibre optical dispersion radar

object

object fibre

Fig. 1: sketch ofthe sensor,

3. "Spectral radar"

Fibre optical dispersion radar

dispersion: 832 mm fibre

I . . . ~TV~v"l

-4~: ~

~v,

wavelength 663.9 669.5 674.8 680.3 685.2 nm distance -D.6 -D.3 0.0 0.3 0.6 mm

Fig. 2: output spectrum ofthe "dispersion radar"

distance

-D.6 mm

-D.3 mm

0.0 mm

0.3 mm

0.6 mm

The spectral radar [5] is again, an interferometer with spectrally resolved output I(k), see Fig. 3a. There is no dispersive element. It can be used for real "optical tomography", in other words, we can measure structural information in Iayered objects or in scattering objects, such as thin film stacks, ceramics, human skin, ... The basic principle is that we store the waves scattered from the object, by the "reference wave~' from the reference mirror. The mathematics is as in holography. By a Fouriertransformation of the (modified) spectrum I' (k), we can reconstruct optical properties along the 'Optical axis of observation, such as

absorption, scattering coefficient ~s, anisotropy factor g.

The output I(k) ofthe "spectral radar" is, basically, given by

I(k) = 1 + f a(z) cos (2 k z) dz (2)

2

with a(k) = scattering amplitude of waves that travelled the distance z. After some symmetrization, by Fourier transformation of Eq. (2), we get a(z), the local scattering amplitude. This local amplitude is shown in Fig. 3b, where the object is "hidden" within a strongly scattering PVC block. The peak of the hidden obstacle surface is clearly detected, although invisible to the human observer. After lateral scanning ofthe object, the shape ofthe hidden metal pin can be discovered as shown in fig. 3c. Figure 3d displays the in vitro measurement of the comea of trout. Figure 3d displays the ability to measure within "dynamic" media with Brownian movement: two wires are introduced within a 25% milk­water suspension. The scattering properties of the suspension are similar to that of human skin. Although the wires are not visible to the hun1an observer, due to the scattering of light

Within 700 !J. suspension, the spectral radar can clearly localize the wires.

Fig. 3a: setup of the spectral radar

(short coherence Jength)

Fig. 3b: Fourier transform­ation ofthe interfer­ometer output I(k). The two peaks re­present the sample surface, and the surface of the metal pin, hidden in strongly scattering PVC.

3

photodlode array

surface

metalpin \

A ~0 100 1~0 ZOO l~O 300 3~0 400 4~0 ~00 ~~0

depth [JUD]

Fig. 3c: lateral scan over the sample surface,uncoveringthe hidden metal pin.

[mm]

Fig. 3d: in vitro measurement ofthe comea of fish (trout)

I I

800 - surface -... r ".

600 - -...

light"

400 I--

... ".

~ 200 I-

... ;..-meta! ".

I I //j p1n

0 0 200 400

depth [J.tm]

lateral coordinate [J.tm]

0 200 400 600 800 1000

____ _,. depth [J.tm]

Fig. 3e: localisation of two metal wires within a 25% milk-water suspension, which has similar scatteringproperties as human skin. There is considerable Brownian motion.

4. Coherence radar for "time resolved" scattering experiments [3]

If we detect the maximum cantrast of the spatially modulated coherence pattem, by sensing it with a moving reference, the effect is similar to time resolved experiments, where the time offlight of photans is measured. W e measure the optical path length of our broad band

4

signal, compared to the reference signal. Since the coherence length of white light is in the range of a few micrometers, the time resolution can be a few femtoseconds. In contrast to short Iaser pulse generation, our technique is quite simple and non expensive. W e just Iook at the image of the object, scan the reference length and separate the coherent fraction in the image, by modulation of the reference phase: The incoherent fraction does not change within subsequent frames, while the coherent fraction displays contrast in the difference image.

Figure 4 displays single frames of a slow motion "film" showing the photons penetrating a surface and travelling through the volume, around an absorbing obstacle. (All black dots are photons that travelled the same path length). Due to multiple scattering, the photons show diffusion within the volume, affecting the possible spatial resolution of such "time of flight" methods.

Fig. 4: frames of a slow motion film about"time resolved" photons propagating in a strongly scattering medium, travelling around an absorbing obstacle

a) b)

+-- 1 mm ~

d)

5. Simulation of scattering experiments with spatially modulated coherence

Simulations can help to understand scattering of photons within human skin, etc. Simulations described in the literature, for example, [6] are purely incoherent, i.e., the photons are just counted. Coherent Superposition is not taken into account. Here we present some results of coherent simulations. W e assume statistically distributed scatterers, where coherent waves with different wavelengths are scattered. W e detect the scattered waves with a coherent reference, as in the experiments described above.

Figure 5a displays single frames of such a simulated scattering experiment. The results are completely consistent with the real experiment (see fig. 4), including the occurence of a "photon horizon'\ that represents the front of the fastest photons.

The coherent simulation is quite costly in terms of computer power. W e tried a very fast incoherent simulation, with only a one-dimensional array of scatterers, to find out, if the results are consistent with the results ofthe spectral radar (sec. 3). N photons are shot into a scattering chain. At each sctterer the photons are transmitted or reflected "With a probability

Pt, respectively, Pr· These probabilities are connected to the anisotropy factor g (g= 1 means

pure forward scattering, g=O means isotropy, g= -1 means pure backward scattering). Each photon returning to the entrance surface is detected and its travelled path length is recorded.

In Fig. 5b the scattering chain simulates a ~s-inhomogeneity: ~s corresponds to the density

of the scatterers. The mean free path length is 1/~s. In the experünent the density of

scatterers changes at depth "10~', from ~s1 = 10 mm-1 to ~s2 = 30 mm-1. The thickness of

the scatterer is "20" units. The simulated result of fig. 5b is quite similar to the experimental results of the spectral radar. The main observation is that the detection of a discontinuity of

~s leads to a strong signal. Furthermore, Strong forward scatterers (g I arge) give better

detection of spatial variations of the scattering properties. This is a valuable result for practical applications in dermatology, where strong forward scattering occurs.

Fig. 5a: coherent simulation of "time resolved" scattering by coher­ence detection. Phot­ons are incident on a layered scattering object. Four frames ( a-d) are shown, that display the propaga­tion of photans in the material.

Fig. 5b: incoherent, one-dimens­ional simulation of a scatterer that is weakly scattering within depth 0-1 0, and strongly scatt­ering from depth 11-2.0. Bold line: strong forward scattering, thin line: more isotropic scattering.

6. Conclusions

"'C 500 .,----------------, C1l

~ 400 - (I) ~ g 300 'öö 1.. J: 200 C1l c. ~ 100 :::l t: 0 -+----+---_l..-__;=::::::=::-J

0 10 20 30 40

travelled pathlength [1 OOJ,Jm]

SOOJ,Jm 1/J,Js = 100 J,Jm

500 J,Jm 1/J,Js = 25 J,Jm

the second layer scatters much more light

~-g=o.sj -g=0.8

It has been shown that the concept of"coherence detection", or "coherence radar", based on

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the prohing of objects with spatially modulated coherence, is a valuable tool. It enables us not only to determine the surface topology of smooth or even optically rough surfaces with

low uncertainty, it is, in addition, possible to acquire data about the morphology of scattering or layered media. Applications in industrial inspection of layered media or in dermatology are straight forward.

Acknowledgment

We greatly appreciate the funding by the BMBF under 13N6667 and 13N6301

References

[ 1] R. Dorsch, G. Häusler, J. Herrmann, Appl. Opt. 3 3 ( 1994) 1306-1314 [2] Th. Dresel, G. Häusler, H. Venzke, Appl. Opt. 31 (7), (1992). 919-925 [3] G. Häusler, J. M. Herrmann, R. Kummer, M. W. Lindner, Opt. Lett. (1996), (accepted) [4] Th. Auernhammer, G. Häusler, ~vf. W. Lindner, Angewandte Optik, Annual Report,

Erlangen, ( 1993) 109 [5] G. Häusler, J. M. Herrmann, M. W. Lindner, R. Ringler, Optik, Annual Report, Erlangen,

(1993) 67 [6] B. Chance, S. Feng, F. Zeng, SPIE, Vol1888 (1993) 78