Theory of Operation for Micro Path Encoders
The Micro Path Encoder has many features made possible by its optical design. It is based on some interesting properties associated with point source diffraction by a grating. The most useful properties occur on a plane which is parallel to the grating and which also contains the point source.
Amazingly, everywhere on this plane we get straight, uniform interference fringes as if we were using two perfectly collimated beams!
The point source can conveniently be approximated by a laser diode (MPE) or an imaged spot from a laser (MPE-X). Figure A below shows light from a near point source whose central ray forms an angle of 30 degrees with the normal of the chrome-on-glass grating.
Figure A. Geometry for point source diffraction
Most of the light simply reflects off the grating but some is diffracted into different orders. The rays from each diffracted order also fan out, and overlap the reflected beam. If we look at a particular point on the target plane, light can arrive there from a multitude of paths. First, from direct reflection, and then from each of the positively and negatively diffracted orders. We can see this in Figure B below. Here too, the central ray has a 30 degree angle of incidence. Plus and minus odd diffraction orders up to 9 are shown. This depiction is for an 8 micron scale and 800 nm light. Figure B. Beam paths taken by diffraction orders in going from source point back to special plane.
Notice, say for the first order, that light which leaves the point source at definite angle to the right of the beam centerline will strike a certain point on the scale to the right of center, and then be negatively diffracted at such an angle that it strikes our target point. Likewise, a ray leaves the point source at a definite angle left of center, strikes a point on the scale left of center, and is then positively diffracted at an angle which causes it too to intersect our target point. The intersection of these rays and the directly reflected beam results in a complex interference pattern.
Figure C shows such an intensity pattern in a 16 by 16 micron region in the center of this target plane. The pattern shows some quite bright areas which align themselves with the central beam direction, 30 degrees. This pattern changes as the scale is displaced in x.
Figure C. Intensity profile at the center of Target Plane
It should be noted that the predominate pattern seen in Figure C, is created from the interference of the zero and first order beams. This pattern cycles every 16 microns in x, and repeats every 8 microns as the linear scale is displaced. However, its amplitude and phase varies across the plane. In fact, there are regions where it doesn't exist.
Let's go back to the interference effects of just two beams, one diffracted negatively and one positively of the same numeric order. This is depicted in Figure D below for n = +/-1. At any point on our target plane the distance traveled by each beam from source to scale to target plane is identical. This means that wavelength variations of the source will not affect their phase difference. It also means that from a design standpoint we may orient our central input angle at any angle which is most convenient.
Figure D. Interference of +n and -n diffracted orders
The incident and diffracted angles are given by the diffraction equation:
The intensity produced from these interfering beams is purely sinusoidal everywhere on the plane. Figure E shows these fringes in the same 16 by 16 micron region. The period is "s" divided by "n", where "s" is the grating spacing and "n" is the order. Further, if the scale is translated along x by s/2n, the position of this sinusoid has moved by one period. So if we move an 8 micron grating by 4 microns, our 8 micron interference pattern has moved by one fringe. The straightness along y and uniformity along x of these fringes only exists on this plane.
Figure E. Intensity profile of first order beams only
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Another very important fact is that if we move the scale closer or further from the point source, i.e., along its normal in the z direction as depicted in Figure A, B, and Figure D, the fringe pattern at the target plane doesn't change its spacing or phase. It doesn't change at all. This scale motion will cause the light which interferes at our target point to have come from different source rays, but they will have diffracted from exactly the same two locations on the scale as before. This means that our measurement system will not be influenced by z-axis translations. Also, since the detected beam is smaller than the length of the scale lines, y-axis translations are likewise ignored. We can sense scale motion using our desired interference pattern by placing a Ronchi grating with the appropriate period right at our target plane. This will "beat" out the pattern we want in the form of a Moire' fringe pattern. Fringe patterns involving other beams yield spatial frequencies which are of no consequence. This too, is quite an important aspect. Our electro-optical system is then composed of very few parts: a laser diode, Ronchi grating and photo-detection. We do not require any beam steering or refractive elements. |
As stated, the fringe uniformity over our special plane means that we may direct our source towards the linear scale at any angle we choose. To maximize the tolerance to yaw rotations we have chosen an angle of 20 degrees in the yz plane for the MPE-B encoders. This is shown below in Figure F.
We use a proprietary detection method to reduce the large amount of DC light which is inherent in our optical design. Scale variations or contaminants will cause DC levels to wander and degrade measurement accuracy. Our detection reduces ordinary scale variations to a level of only 1.5 nanometer! This is well below our standard, minimum resolution of 0.01 micron.
This is accomplished without using more expensive phase gratings as our linear scale. Such gratings are often used to suppress DC light.
Figure F. Layout for the MPE-B
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We then have a position sensor which is impervious to wavelength variations, atmospheric effects, off-axis translations, strongly resistant to contamination, and has wide alignment tolerances. In addition, this is accomplished using very few components. By using the unique properties on our special plane, we end up with a measurement device which is accurate, stable, reliable, and economical. |
