Study on a New Method for Improving Resolution of Grating Interferometer Displacement Measuring System

A method for improving resolution of grating interferometer displacement measuring system is developed in this paper. The measurement system consists of a grating interferometer and a phase-shift device. Two interference fringes are required in the detecting field of photoelectric sensor. If we change the signal phase of the interference fringe by moving the photoelectric sensor between the two interference fringes, the displacement equivalent converted from the photoelectric sensor will changed. The method is applied in positioning system and the experiments’ results indicate that the new displacement measuring method will improve the positioning accuracy about 33%. Also, the errors in the positioning process with the new method are discussed in briefly.

Displacement measuring system based on grating interferometer is often used in traditional precision positioning process [1,2] .Although laser interferometer is better than the former in measurement resolution, it is limited in application sometimes because of its strict requirements on temperature, humidity and so on [3][4][5] .And coarse/fine dual-stage manipulators are widely studied and applied for long distance movement and high precision, [6][7][8][9] though following with complicated mechanisms.Therefore, grating interferometer is selected as the study object in this paper.Usually the measuring resolution of grating interferometer is no better than 0.5 micrometer and it maybe reach to 0.1 micrometer or even smaller if the grating stripe signals are treated with subdivision method, whose subdivision level is limited by the stripe quality [10] .In this paper, a phase shift method applied on grating interferometer stripe is developed and it will get higher displacement measuring resolution in ultra-precision positioning system.
The whole displacement measuring system with grating interferometer consists of a laser device, a blazed diffraction grating, a beam splitter with equal optical path and a photoelectric sensor, as shown in Fig. 1.The parallel incident light launched from the laser device will be split into two beams, transmitted light and reflected light, when it meets the plane O-O of the splitter.When the diffraction grating is in the case of auto-collimation, the two beams will be both diffracted back and will meet together at point C. Therefore, the interference fringes will appear in the place where the two diffraction beams overlap.
The diffraction grating as reference grating is mounted on a linear table.When the linear table moves, the interference fringes will be light and shade in circle and it will be detected and converted into pulse signal by the sensor placed at E point.Therefore, we can control the motion of the linear table by counting the fringe pulses from the interferometer.When the reference grating (or linear table) shifts Δx along the direction shown in Fig. 1, the phase variation of the two coherent light beams is [11] : Where m is the diffraction order and A is the space of the reference grating (for example 1/300mm).
If Δx = A and m =2, then × = π ΔΦ Namely, when the reference grating moves one space, there will be 4 fringe-signals.Therefore, the equivalent displacement to one fringe is: It is important to ensure that there are only two interference fringes, whose distance between them is w, in the detecting field illustrated in Fig 2 .The w value can be changed by adjusting the interferometer.It is regarded that the fringe phase signal is divided into unlimited parts from 0°to 360° in electrical degree and the parts are distributed averagely between the two fringes in theory.Therefore, if we change the position of the photoelectric sensor, the phase of the fringe signal will be changed correspondingly.
Therefore, the increment of fringe signal can be expressed as: Where, Δw -----phase shift w -----distance between the two fringes in the detecting field When the positioning table feeds forward, the interference fringes will move up or down.When the direction of the sensor motion is opposite to that of the fringes, the minus sign is chosen in expression (3).On the contrary, the plus sign is chosen.If ac = 0.83μm, Δw=10 μm and w=10mm, then da=0.83nm.A precision positioning system with grating interferometer displacement measuring device is developed.The whole system is composed of a precision positioning linear table, a set of precision grating interferometer device, a fringe phase-shift device and a computer control system.The block diagram of the system is shown as Fig. 3 and the photo of the positioning system is shown as Fig. 4. The displacement of the precision positioning table is converted into pulses by the grating interferometer and the pulses is counted by counter and finally they go into industry computer.
The precision positioning linear table is the PLS-85 DC linear platform, a product of PI of Germany, with 50nm increment.The core part of the precision grating interferometer device is a high precision diffraction grating with 300 lines per millimeter (or space 3.33μm).The fringe phase-shift device, whose precision accuracy is 1μm, is a linear driven by voice coil motor and controlled by Elmo controller.
In order to validate the stripe phase shift method on displacement measurement, some positioning experiments with laser interferometer as measuring reference has been done on the precision positioning The positioning point is selected at the point of 4mm in the experiments.For example, in the 4mm experiments, 4000μm/0.83μm= 4819.3pulse.Therefore, the positioning error of traditional method is 0.23μm in theory.In the experiments of new stripe phase shift method, after receiving 4818 pulses, the photo electric sensor will move and the positioning error of new method is 0.09nm in theory.Actually, the error is bigger than 0.09nm greatly because of the positioning errors of linear  The contrastive results on the positioning experiments with traditional method and new method are shown in the table.It indicates that the fringe phase shift method will improve the positioning accuracy about 33%.
There are errors in the positioning process: The actual displacement error of the phase-shift mechanism is less than ±0.5μm.Therefore, when the phase shift displacement is 10μm, the resolution error will be less than 10 percentage of the academic value.
The transfer function of the grating interferometer can be calculated in the case of the space error being used as input value [2] .Supposing a concentrated error a Δ is in the x 0 position of the reference grating, it will be distributed in the area with width from (x 0 -d) to (x 0 + d) by the grating interferometer (d, the width of the light beam that irradiates on the reference grating).Namely, the concentrated error a Δ will be reduced to a Δ /2d.For the concentrated error is reduced many times, it has little influence on the positioning process.
The other factors, including the distance accuracy between the two interference fringes and some environment factors such as vibration and temperature in the working field, will bring errors also.Especially, the vibration from the base of the system will often bring gross errors.The gross errors in the experiments (such as the traditional method 3 and 5 on the table of measurment results) should be eliminated by digital filtering.
A new ultra-precision displacement measuring method, based on fringe phase shifting method, for grating interferometer displacement measuring system is developed.The core parts of the system is a grating interferometer and a phase-shift device.When the signal phase is changed by moving the photoelectric sensor between the two interference fringes in the view field, the displacement equivalent converted from the photoelectric sensor will changed correspondingly.Therefore, the new method could be applied in positioning system: supposing the photoelectric sensor is moved 10μm, (the traditional resolution is 0.83μm and the distance between the two fringes in the detecting field is 10mm), then the resulution of the positioning system will be 0.83nm,.namely,the resolution is 1000 times than that of the traditional method in theory.The experiments using the new method have been done and the results show that it will improve the positioning accuracy about 33%.Also, the errors in the positioning process with the new method are discussed in briefly.It indicates that the displacement accuracy of the phase-shift mechanism, the space error of the reference grating and other factors such as vibration will influence the displacement revolution of the positioning process. [

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Fig. 2 Phase shift of interference fringeFront viewSide view

Fig. 4 .
Fig. 4. The photo of the positioning system table itself and other factors.