Fiber Optic Confocal Sensor for Probing Position, Displacement and Velocity

Transcription

1 1 Fiber Optic Confocal Sensor for Probing Position, Displacement and Velocity E. Shafir and G. Berkovic Electro-Optics Division Soreq NRC Yavne 81800, Israel Abstract We describe a fiber optic confocal sensor (FOCOS) system which uses an optical fiber and a lens to accurately detect the position of an object at, or close to, the image plane of the fiber tip. The fiber characteristics (diameter, numerical aperture) and optics (lens F/#, magnification), define the span and precision of the sensor, and may be chosen to fit a desired application of position and displacement sensing. Multiple measurement points (i.e. fiber-tip images) may be achieved by use of multiple wavelengths in the fiber, so that each wavelength images the fiber at a different plane due to the chromatic dispersion of the optics. Further multiplexing may be achieved by adding fibers on the optical axis. A FOCOS with multiplexed fibers / wavelengths may also be used for velocity measurements. OCIS codes :

2 2 Introduction Confocal imaging is a well established technique in high resolution microscopy which can also be adapted for sensing applications 1. In confocal imaging, light emerging from a small aperture is imaged by low F/# optics into a small object volume, and information is obtained via the light back-scattered through the same optics and aperture. Several confocal sensor systems have been reported in which the illumination/detection aperture is an optical fiber 2,3,4 A common application is surface contouring or profilometry, where the sensor is scanned laterally over a surface, and the height adjusted to give the maximum confocal signal at each lateral position 1,3,4. In this article we discuss the use of a fiber optic confocal sensor (FOCOS) to probe the position and displacement of objects. We consider optics, stand-off distances and measurement ranges which are in general larger than those used in profilometry applications. Furthermore we introduce multiple-fiber and multiple-wavelength techniques which further expand measurement range, and allow other sensing applications, such as velocity measurements. Other attractive features of the sensor are simplicity and fast measurement. The Principle When the light emerging from the tip of an optical fiber is imaged by a lens towards an object, the same lens can act to "confocally" collect light reflected/scattered from the object back into the fiber. As shown in Figure 1, this process is most efficient when the object is located precisely at the image plane, and the efficiency decreases when the object is displaced, in either direction, from the image plane.

3 3 (i) θ a z (ii) Figure 1 : Principle of fiber optic confocal sensor (FOCOS) for object at the image plane (i) and displaced from it (ii). z The intensity of light back-reflected to the fiber is therefore a function of the displacement ( z) of the object from the image plane defined for the fiber positioned at distance a from the lens. By appropriate choice of the optics, we can control the width of the response (i.e. the fall off of the signal with z) to be either sharp or broad. This allows us to tailor the response according to the specific needs of a given application, which may require high resolution (i.e. sharp localization) over a short range of displacements, or conversely, lower resolution over a broader range. This latter application relies on retrieving the object position from the light intensity back-reflected into the fiber, i.e. a straight-forward intensity sensor. Due to the well known limitations of intensity-based sensing 5 (such as source fluctuations, drifts), we have decided to concentrate our research on the former case; that is constructing a sharp-localization system and retrieving the object location only when it traverses the exact image plane, to within the FWHM of the back-reflected signal. Besides its simplicity, the main advantage of the sensor is its fast response, limited only by the detector bandwidth, which extends the use of the sensor to very fast moving objects, e.g. in ballistic research applications.

4 4 Design Considerations The resolution and "depth of field" of a FOCOS sensor are connected to the "localization" of the sensor signal, which may be defined as the FWHM range of displacements for which the object returns light to the fiber. In order to understand the relationship between the optical parameters and the localization of the FOCOS signal, we have calculated for specific model cases the relative signal as a function of z. Intuitively, the response will be a function of the following parameters: (a) Fiber core diameter (d core ) (b) Cone of illumination of the lens (θ) by the fiber, which will not exceed the fiber numerical aperture (NA) (c) (d) Lens parameters: focal length, diameter (F#) Optical magnification, given by the ratio z/a Full numerical calculations may be performed rigorously using optical design software or detailed models for confocal imaging 6,7,8, but for illustrative and instructional purposes we will consider a simple geometric model which may be solved analytically. This model proceeds as follows i) For an object position displaced from the focal plane by a small amount z, the spot size on the object is calculated using the conical ray model as in Figure 1. Further refinement, to be applied for single mode fibers, includes diffraction corrections (2.44*λ*F#). ii) From this spot size and object position, we calculate its corresponding image size and position when back reflected/scattered towards the fiber (the ellipse in Figure 1-ii). iii) Considering the back-scattered rays forming this image, the fraction of these rays which enter the fiber core is calculated.

5 5 Some typical results are given in Figure 2 and Figure 3, showing how varying a single parameter taken from the four parameters listed above influences the FWHM of the FOCOS signal detected as the object passes through the image point. Note that the model assumes an ideal (diffraction limited) lens whose thickness is neglected. The conclusions reached were that the peaks become shaper as the fiber diameter decreases, as the fiber NA decreases, as the lens F/# decreases and as the optical magnification decreases. Figure 2 and Figure 3 illustrate these conclusions Single lens imaging, F#=1 diff. lim. asphere (8mm dia) 10 micron NA=0.12 fiber 50 micron NA=0.12 fiber 100 micron NA=0.12 fiber Throughput Distance (mm) Figure 2 : Comparison of calculated FOCOS signals for various fiber core diameters (10 µm, 50 µm, 100 µm) assuming a white, diffusive object, fiber NA=0.12, a diffraction limited, thin 8mm focal length F/1 lens, and fiber positioned 33 mm from the lens (magnification = 0.32).

6 magnification 0.32 magnification 1.14 Rel signal z position (mm) Figure 3 : Comparison of calculated FOCOS signals and their widths for different magnifications. We consider a white, diffusive object, 50 µm core fiber with NA=0.12, and a diffraction limited, thin, 8mm focal length F/1 lens. The fiber is positioned either 33 mm (full curve) or 15 mm (broken curve) from the lens (magnifications of 0.32 and 1.14 respectively). For demanding applications, requiring high precision of the order of 10 µm, it will be necessary to achieve the narrow responses simulated in Figure 2. As stated above, this will occur for small values of NA, F/#, d core and optical magnification. In choosing operational values for the above parameters for a real experiment or application, one has to take into consideration several additional factors, namely: (i) A practical minimum of near 1 for the F/# of a single lens, and the need for neardiffraction-limited optics. (ii) A practical minimum of about 0.1 for fiber NA (iii) At very low magnifications (< 0.3) the fiber will be too far away from the lens, and thus much of its light will miss the lens, leading to loss of signal. (iv) In displacement or motion sensing of objects with rough surfaces there may be a problem with the use of very small diameter fibers (e.g. single mode fiber) combined

7 7 with low magnifications. The spot diameter on the object (at the image plane) should be greater than the surface roughness of the object, otherwise the reflected signal will be prone to erratic and irreproducible fluctuations according to the local geometry. Experimental Results with Single Fiber In this section the principle of the FOCOS technique and its ability to tailor the width of the response according to the optical parameters discussed above will be demonstrated. Our experiments used the setup shown in Figure 4, where light is sent through a 2*2 fiber coupler and imaged by the lens towards the object in this case a mirror. The FOCOS signal coupled into the fiber passes through the same coupler sending half the light to an amplified photodiode detector or power meter. The source is the ASE of an Er 3+ doped fiber, centered at 1531 nm, with a spectral FWHM of 4 nm, and an output power of about 6 mw. The spectral broadness of the source eliminates unwanted coherence effects. The fiber couplers used either SMF-28 fiber (9 µm core, NA=0.11) or graded index MM fiber (50 µm core, NA=0.20). When connecting the source to the MM fiber coupler, we did not make any special efforts to fill all the modes of the fiber, and thus the coupler may not have equally split the outputs. The FOCOS signal is measured as the mirror is slowly translated in a controlled step wise fashion through the image plane. For simple lenses, our requirements of low F/# and near-diffraction-limited performance are mutually exclusive. However, these requirements may be met either by using an aspheric lens, or by using multiple lenses with spherical aberration correction. The former is preferred for small diameter optics (typically < 10 mm), while the latter is more practical for larger diameter optics. In our studies, we have used commercially available F/1 aspheric lenses (Thor Labs C150TM-C, C240TM-C of focal lengths 2mm and 8mm respectively) which may be employed for imaging at distances of up to 20 mm from the lens. We also have verified our concept with aberration corrected 1" diameter F/1 optics, using a pair of doublet lenses (Thor Labs, LAC-382C) enabling imaging at longer distances.

8 8 Source a z Coupler Lens Object Detector Gel Figure 4 : Set up to test and demonstrate the FOCOS technique. The unused output port of the coupler is coated with index-matching gel to eliminate back reflection to the detector. Concentricity and parallelism of the active output fiber (terminated in a standard FC-type connector) and lens axis is ensured by mounting both components in a cylindrical lens tube. We present typical results for two F/1 aspheric lenses in Figure 5 - Figure 6. In these Figures, we show results for magnifications of around 1/3, which we consider to be the optimum when a narrow response is required, without sacrificing signal for a fiber of NA < The target object is a metallic mirror on a micrometer controlled translation stage. Due to the large angle of collection, no precise mirror alignment is required. The aspheric lenses indeed yield sharp responses of widths around 60 µm with the SMF-28 fibers, and, as expected, a larger width for the 50 µm fibers. These results correlate well with our simulations see Figure 2 - although (unsurprisingly) the experimental response widths are slightly larger than for the idealized and simplified simulation, which is used for illustrative purposes only. Note that the FOCOS response signals consist of a flat background due to the Fresnel reflection from the active fiber end. Due to the low source coherence, there are no interference effects between reflections from the fiber tip and object. The fiber tip reflection can be eliminated by an angled cleave, although this will often also be accompanied by a decrease in the FOCOS signal due to the angular offset between the fiber axis and the emission and acceptance cones.. In Figure 7 we show how the FWHM increases as a function of the optical magnification (z/a in Figure 4) for the 50 µm fiber. The geometric optics model predicts a quadratic dependence, which is observed at

9 9 high magnifications. At low magnifications, when Gaussian beam effects, diffraction and lens imperfections are significant, the experimental width is larger than the prediction of this simplified model. 1.2 SM fibers - FWHM approx 60 µm MM fibers - FWHM approx 90 µm 1.0 Relative Signal Mirror Displacement (µm) Figure 5 : FOCOS signal at 1/3 magnification using 2 mm diameter F/1 aspheric lens C150TM-C and (a) SMF-28 fibers (b) 50 µm MM fiber. The fiber is positioned approximately 8mm from the lens, and the object mirror is optimally imaged at a distance approx 2.7 mm from the principal plane of the lens. Thus the effective NA for the MM fiber is 0.12, essentially the same as for the SM fiber. 1.2 SM fiber ; FWHM = 60 µm 50 µm MM fiber ; FWHM = 110 µm 1.0 Relative Signal Mirror Displacement (µm) Figure 6 : FOCOS signal at 1/3 magnification using 8 mm diameter F/1 aspheric lens aspheric lens C240TM- C and (a) SMF-28 fibers (b) 50 µm MM fiber. The fiber to lens distance is 30 mm, and imaging occurs approx. 10 mm from the lens. Thus the effective NA for the MM fiber is 0.12, essentially the same as for the SM fiber.

10 10 FWHM (µm) magnification (m) Figure 7 : Dependence of FOCOS signal FWHM (squares) on magnification for 8 mm diameter F/1 aspheric lens C240TM-C and 50 µm MM fiber. The peak FOCOS signals approach that of 100% efficiency of collection of reflected light by the fiber. The dashed curve is the prediction of the simplified geometric model. Figure 7 shows that if a narrow FWHM is required, the FOCOS system must be operated at low magnifications (<0.5). This means that the object distance from the lens can be up to 1.5 times the focal length. Thus the 8mm diameter F/1 lens used in Figure 7 is able to produce narrow FOCOS signals for probing distances of up to about 12 mm. In order to test the FOCOS principle at longer distances, we demonstrate system performance with 1" diameter F/1 optics. In Figure 8, we show the response for an imaging system comprising a pair of doublets, each with 50 mm focal length and 25 mm diameter to give an overall F/1. The FOCOS response width is about 180 µm, about a factor of 2 larger than for the 2mm and 8mm diameter F/1 aspheres with the same 50 µm fiber.

11 Relative FOCS Signal Mirror Displacement (µm) Figure 8 : FOCOS signal using 1" diameter F/1 optics (pair of doublets LAC-382C). The 50 mm fiber is placed 90 mm from the closest lens, and in order to be imaged, the mirror must be positioned approximately 35mm from the lens. The inset shows the arrangement of the two doublet lenses. Multi-Fiber principle A single fiber FOCOS system can be used as a single-point position/displacement probe, with a precision that can be expected (on the basis of reasonable signal-to-noise) to be an order of magnitude smaller than the FWHM. Thus, when the response width is narrow (of the order of 100 µm) the sensor can yield high precision, of the order of 10 µm. An obvious extension of such a system would be to add measurement points (fiber tip images). This may be realized by employing several fibers at different distances from the lens, each of which will probe its own image point in the region of interest. The principle is shown in Figure 9 for either two or four fibers, using the same optics.

12 12 Figure 9 : Schematic of set-ups with (a) two and (b) four fibers for distributed sensing of the object position. In practice, use of multiple fibers with a single lens as shown in the figure will induce some small differences from the single-fiber case. Firstly, it is only possible to place one fiber precisely on the optical axis defined by the lens; the other fibers (and their image "points") will necessarily be off axis by differing amounts and polar angles. However, the fibers may be packed closely together, so that they are off axis by not more than a few hundred microns, and their images will be off axis by smaller amount (for magnifications < 1). Furthermore, small deviations of the fiber from the optical axis should not significantly change the performance of the lens with regard to the fiber imaging. The second difference when using multiple fibers with a single lens is that the acceptance/emission cone of each fiber (except the one closest to the lens) will be partially obscured by the fibers in front of it. This fractional obstruction will occur twice, as both the light emitted by the fiber and the back scattered FOCOS signal will be affected. Of course, when different physical points on the object are to be probed, the fibers may be staggered appropriately in the lateral plane. However, for fibers whose lateral displacement is significant relative to

13 13 the lens diameter, the fidelity of the optics under off-axis imaging conditions must be considered. For large objects one might use a separate imaging lens for each fiber, rendering all these issues not relevant. Obviously these two approaches may be merged and a compound system, comprising several lenses - each with laterally staggered fibers - may be applied to multi-position sensing of objects. Multi-Fiber Experiments We have demonstrated the multi fiber principle using two fibers as shown in Figure 9(a). In these cases, the two fiber ends were stripped and cleaved and the fibers held together so that they both could be as close as possible to the lens axis. In Figure 10 we show results for two 50 µm fibers, positioned 105 mm and 90 mm from a pair of LAC382-C doublets. As seen in the Figure, the two doublet lenses are arranged so that the sharply curved surfaces point inwards towards each other. Two peaks are observed, corresponding to the mirror positions at the image planes of the fibers. Both peaks, which are separated by 1.68 mm, exhibit a FWHM of about 300 µm.

14 14 50/125 µm fibers 1 inch lens tubing 15 ca. 90 mm Signal (V) mm Rel Mirror Displacement (microns) Figure 10 : A two-fiber FOCOS sensor, using 50 µm core fibers, and two LAC-382C doublet lenses giving 25mm focal length F/1 optics (top). The bottom curve is the response signal for a mirror, initially 35 mm away, translated towards the sensor. Multi-Wavelength Principle A complimentary approach to on-axis fiber multiplexing is to use multiple wavelengths of light. Due to the chromatic dispersion of the focusing optics, the image point of the fiber in a FOCOS sensor will vary along z with the wavelength, thus a distinct image of the fiber tip will be created for each wavelength, as if other fibers were added, exactly on the optical axes. Although these chromatic effects are generally considered to be an undesirable aberration is optical systems, this property may be exploited (and even deliberately enhanced) for the configuration just described. The chromatic dispersion of the optics has

15 15 previously been utilized in confocal sensors, some of them in combination with optical fibers, using continuous broadband light sources and some sort of spectral analysis 4,9,10. Our approach is to use several discrete wavelengths with simpler and in-built spectral discrimination 11. The chromatic dispersion effect in the 8mm focal length F/1 asphere C240TM-C used in Figure 6 is readily demonstrated. A series of experiments was performed using the set-up of Figure 4 with various wavelength sources (i.e. a separate experiment for each wavelength). In all experiments, the fiber tip is held in the same fixed position, 25 mm from the lens. In Figure 11 we show results for 6 different wavelength sources from 532 nm to 1531 nm. The peak shifts monotonically over about 700 µm, and the observed shifts match well the expected shifts calculated on the basis of the known chromatic dispersion of the lens material. The individual peaks exhibit FWHMs of µm, and their combination permits position sensing over an extended range of close to 1 mm.

16 (a) 1310 nm 1064 nm 833 nm 635 nm Normalized Signal nm 532 nm Rel Mirror Position towards Lens(µm) (b) 532 nm Experimental shifts (µm) nm nm nm nm Calculated Shifts from 1531nm peak (µm) Figure 11 : FOCOS signals using different wavelength sources. The 50 µm MM fiber tip is 25mm from the 8 mm diameter F/1 aspheric lens aspheric lens C240TM-C. Each curve represents a discrete experiment using a single wavelength. (a) FOCOS signals as a function of mirror position. The zero reference position is the mirror position giving the FOCOS peak with the 1531 nm source, at a nominal distance of 12 mm from the lens. (b) Plot of observed shifts of the FOCOS peak with wavelength versus calculated shifts. Although the results presented in Figure 11 were obtained from six discrete experiments, each using a single (different) wavelength, it is straight forward to apply the idea to simultaneous measurements. This may be achieved by multiplexing several wavelengths at the input to the probing fiber and optionally demultiplexing them at its output.

17 17 Of course, one may multiplex both fibers and wavelengths. This is demonstrated, for the simplest case, in Figure 12 which shows a simple set-up and results, using two fibers and two wavelengths, to give four image points along the axis. Four peaks are clearly observed as two pairs about 3mm apart (due to the two fibers) while the peaks in each pair are separated by about 0.7mm due to the wavelengths difference between the two sources and the chromaticity of the optics. Note that the optics used (a pair of LAC- 382C doublets) is designed to be "achromatic" in the visible range, but not in the infra-red. 980 nm 50/125 µm fibers and couplers ca. 17 mm ca nm Detector mm 800 Signal (mv) mm 3.96 mm Relative Position (µm) Figure 12: Set up for a FOCOS sensor using two fibers and 2 wavelengths. The lenses are a pair of LAC- 382C doublets giving F/1 optics of 25mm focal length. The results show four peaks as the mirror is translated towards the sensor, the peaks at 0mm and 3.38 mm come from the 1531 nm light (with the longer effective focal length) while the other two peaks come from the 980nm light.

18 18 Dynamic FOCOS multifiber experiment A multiple fiber/wavelength FOCOS system can be used as a velocity probe by detecting the time lapse between passage of the object at the image points originating from either two fibers or one fiber and two wavelengths. Note that this sensor measures velocity in a direction parallel to the optical axis, as opposed to "traditional" imaging of motion normal to the optical axis 12. In order to demonstrate velocity measurement, we have used a home-built system where switching an electro-magnet propels a lever by about 10mm. We mounted a reflective metal plate on the lever, and positioned the two-fiber FOCOS sensor with 1" optics described in Figure 10 at a starting distance of 40 mm from the lever. The FOCOS output was fed into an amplified InGaAs detector (Thorlabs P/N PDA255-EC) and oscilloscope. When the lever was propelled by the electromagnet, a signal shown in Figure 13 was recorded. The dynamic trace clearly mimics the slow step-wise calibration shown in Figure 10. The time between peaks is 0.75 msec, corresponding to an average velocity of 2.3 m/sec. Figure 13 : Dynamic FOCOS signal as recorded on an oscilloscope (horizontal scale 500 µsec/division) using the two-fiber (single wavelength) FOCOS sensor shown in Figure 10. The dynamic experiment is described in the text.

19 19 Conclusion A fiber optic confocal sensor has been described, which can deploy multiple fibers and multiple wavelengths for multiplexing imaging points. Applications to position and displacement sensing, and velocity measurements have been demonstrated. Acknowledgments The authors thank S. Rotter and A. Schoenberg for help in some of the early modeling and experiments, and G. Appelbaum for assembling the moving target in the dynamic experiment.

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