Investigation of an optical sensor for small angle detection

Investigation of an optical sensor for small angle detection usuke Saito, oshikazu rai and Wei Gao Nano-Metrology and Control Lab epartment of Nanomechanics Graduate School of Engineering, Tohoku University Sendai, 98-8579, Japan Tel.: & Fax: +8--795-6953 E-mail: saito@nano.mech.tohoku.ac.jp bstract In this article, we describe the evaluation result of the characteristics of the angle sensor based on laser autocollimation method especially focused on the result ab the evaluation of the relationship between the sensor sensitivity and measurement point of the target. The sensor consists of a laser diode (L) as the light source, and a quadrant photo diode (QP) as the position-sensing detector, and it requires a light-reflecting flat surface like a small plane mirror as a target. This optical system has advantages of high sensitivity, high resolution, quick response and the ability for -axis angle detection. Generally, the angle sensor only responds angular displacement of the target mirror, so the characteristics of the angle sensor such as sensor sensitivity are not influenced by the position of the target even if the target moves along with the optical axis. On the other hand, the sensor sensitivity could be changed according to the position of the target. Main error components that influence the sensor sensitivity are proposed and the optimal conditions of the optical system of the sensor are analyzed. The experimental result ab evaluation of the working distance is also presented. Keywords: Laser autocollimation method, sensor sensitivity. Introduction Recently, precision components such as precision optical elements and semiconductor are widely used and this encourages the progress of the precise motion control. The key component of such precise motion system is the ultra-precision stages which are often applied in precision machine, semiconductor manufacturing machine and precision inspection device, etc. Therefore, the measurement of movement errors of the stages is essential for evaluating the performance of those machine tools. The movement errors of the stage can be expressed as the positioning error and translational motion error (straightness) along the moving direction. The former error can be measured by using the laser interferometer or linear encoder, and the latter one is usually measured based on the straightedge. dditionally, the positioning error includes the angular motion errors that exist to cause unexpected bbe-errors. The simple way for measuring simultaneous two-axis angular motion errors such as pitch ( ) and yaw ( Z ) is feasible by using the laser autocollimation method with twodimensional position-sensing detector [, ]. Since this method has the advantages of high sensitivity, quick response and high resolution, it can be satisfy the key requirements for applying to the ultra-precision profile measurement such as flatness measurement of large silicon wafers [3]. nd this method can be applied for measuring the dynamic angular motion errors such as precision stages because of its fine measurement capability. For the purpose of measuring the angular motion errors precisely, it is necessary to evaluate the working distance of the angle sensor which determined as the distance between the angle sensor and the target reflector. -8

g. Principle of the angle detection Fig. (a) shows the schematic view of the laser autocollimation method. The L is used as a light source. When the target mirror has inclination angle, the corresponding optical spot displacement is occurred on the focal plane of the objective lens. The relationship between the incident angle and the optical spot displacement d V_ is expressed by the following equation: dv _ dv _ arctan () f f where f is the focal length of the objective lens, the and the d V_ are assumed to be very small in the Eq. (). It is possible to calculate the change of the tilt motion of the target mirror just by detecting the change of the spot position d V_ on the focal plane. s can be seen in this figure, the QP is adapted as the position-sensing detector, so this optical system is able to measure two-directional angular displacements simultaneously. Fig. (b) shows the schematic of the spot behavior on the QP cells when the angle has changed. ssuming the laser beam has a circle shape and a Gaussian distribution of intensity, the spot size on the QP can be obtained as follow equation [4]: f r Kt () where and r are the beam diameter and optical spot diameter defined as a full width at /e maximum value (FW/e M) of the beam intensity. nd f is the focal length of the objective lens and is the wavelength of the L. The K t is a Gaussian beam truncation ratio [4] and can be derived by the ratio of beam diameter and aperture size of the objective lens. The QP has insensitive area (gap) between P cells in H and V directions. Now assuming there is only H-directional gap, the photocurrent of each P cells are proportional to the optical spot receiving area on each P cells, and the current conversion sensitivity of each P cells will also be constant. Output from the QP can be expressed as follow equation: ( I I ) ( IC I ) ( S S ) ( SC S ) % % (3) I I IC I S S SC S where I, I, I C, and I are the photocurrent of each P cells, and S, S, S C and S are the optical spot receiving area of each P cells. ividing by the total put value can compensate for the change in the intensity of incident light. When the target mirror has inclination angle of Δθ, the optical spot displacement d V_ occurs coincidentally on focal plane of the objective lens as expressed in Eq. (). The difference between incident spot areas of cells, and C, can be approximately expressed as 4r d V_. Moreover, the entire area of an optical spot is r -4r g, so the Eq. (3) can be rewritten as follows: Plane mirror Z Z Z X Objective lens QP cells d V_ Emitting area on P cell S, S, S C, S I V I S S d V_ Incident beam Working distance f V H Spot (a) Principle of the laser autocollimation method (b) Optical spot on the QP (d V_ -direction) Fig.. Geometrical model for optical angle detection. I S S C r C I C H QP cells -9

Sensor put 5 %/div 4r dv _ 4dV _ % % (4) r 4r g r 4g The sensitivity of the angle sensor S can then be roughly approximated as the ratio of incident angle Δ and sensor put, and is expressed as follow equation: 8 4 Kt g S % (5) f It can be found that the sensitivity could be influenced by the gap size of the QP, and the larger the gap size g is, the higher sensitivity S can be obtained. On the other hand, it worth noting that the enlargement of the gap size reduces the optical spot receiving area on each P cells, and it causes the decrease of signal/noise ratio of the sensor signal put. 3. nalysis ab the relationship between sensitivity and working distance -axis angle sensor for evaluation of its fundamental put characteristics has been fabricated. Fig. 4 shows an example of the experimental setup for evaluation of the sensor sensitivity and its working distance. In this sensor, laser beam is emitted from L and collimated through the collimate lens and mm aperture. Then after being reflected by the plane mirror mounted on the -axis PZT driven tilt stage, the laser beam goes through the objective lens (triplet lens with f = 5.4 mm) and focused on the focal plane, forms a optical spot there. nd the QP with m gaps is used as its position-sensing detector. The target mirror can generate -directional tilt angular motions (, Z ), and these motions are detected by the angle sensor and commercial autocollimator (PS, Nikon Corp.), simultaneously. The analog put from the commercial autocollimator is used as the angle reference for evaluation of the put of the angle sensor. Fig. shows the experimental result ab put of the angle sensor. In this experiment, the sinusoidal signal is applied to drive the tilt stage, and the sensor puts at different measurement point are evaluated. In Fig., the horizontal axis is the applied angles measured by the commercial autocollimator and the vertical axis is the puts from the angle sensor. The two sensor puts (x = 5 mm, 35 mm) are linearized and the fitting line are plotted in -axis angle sensor Working distance Mirror X Z Commercial autocollimator Optical rail -axis PZT driven tilt stage Fig. 4. Experimental setup of the -axis angle sensor. x = 5 mm (Sensitivity.44 %/arcsec) x = 35 mm (Sensitivity.589 %/arcsec) ngle 5 arcsec/div Fig.. Comparison of the sensor puts. Fig. 3. Optical model for analysis. -

±5 arc-seconds measurement range. The sensor sensitivities are expressed as the inclination of the fitting lines. From this experimental result, the sensor sensitivity could be changed ab % according to the position of the target mirror, i.e., the sensor put is influenced by the target movement. s expressed in Eq. (4), the sensor put is affected by the displacement d V_ and the size of the optical spot on the QP cells. So the main components affects the sensor put are analyzed. Fig. 3 shows the schematic diagram of the error components. The collimated Gaussian laser beam propagates through the air toward X- direction has the beam spreading because of the diffraction effect. The beam diameter at a measurement position x is expressed as follow equation: x 8 x (6) where and are the FW/e M beam diameter, and the beam waist is assumed to be on the open end of the collimate lens. From Eq.() and Eq. (6), the diameter of the optical spot could be changed at different measurement position x. nd another component is the defocus amount x. The spot displacement d V on the defocus plane is expressed as: x x dv x, x f x tan( ) f ' x, x (7) f When x > f is effective, this component works for increasing / decreasing the put of the angle sensor depends on the sign of the x. dditionally, the optical spot is also enlarged by x. From Eq. (6), the enlarged optical spot size r is calculated as follow equation: 4x r x, x r x (8) r x The enlargement of the spot size r against the gap size g increases the optical spot receiving area on each P cells, so the signal/noise ratio of the sensor signal put also improves. The sensor sensitivity S based on these two error components is calculated by substituting Eq. (7) and Eq. (8) to Eq. (4): 8 f ' x, x S x, x (9) r x, x 4g The computer simulation has carried to estimate the influence of these components and find the optimal optical conditions that minimize the change of the S against the measurement position of the target mirror. The simulation conditions are shown in Table. In this simulation, the optical system is an aberration-free system, the beam shape assumed to be a circle and only consider ab Gaussian beam propagation (TEM beam mode). The sensor sensitivities S at each measurement position (x = mm - 5 mm) are calculated and took the average under the different combination of the optical conditions shown in Table. The deviation from the average sensitivity is determined as V am_d. Fig. 5 shows the simulation result. The horizontal axis shows the defocus amount x and vertical axis is the deviation V am_d. The optical conditions are chosen as f = 5. mm, g = 5 m, measurement rang is ±5 arc-seconds and other conditions are same as shown in Table. From this result, when the initial beam diameter is larger, the influence of the beam spreading expressed Eq. (6) becomes smaller, and the influence of the defocus amount x may dominate the change of the sensor sensitivity. When the initial beam diameter = 3. mm, the deviation V am_d is under.3 % over the range of x from - m to + m. This result also indicates the tolerance of the QP positioning is high when large is chosen for the initial diameter. -

eviation from average sensitivity Vam_d % eviation from average sensitivity Vam_d % Table. Simulation conditions. Focal length of the objective lens f = 5.4 mm, 5. mm. QP gap size and active area Gap size : 5 m, m. ctive area : 5 m 5 m. Condition of the incident beam : mm, mm, 3 mm. : 683 nm. Position of the target mirror X : mm 5 mm (calculation of each 5 mm). efocus amount x : - m + m (calculation of each 5 m)..5 3..5.9 =. mm.5.6 Z.3 = 3. mm.5 - -5 5 efocus amount x mm Fig. 5. Simulation result of deviation of the sensitivity. 3 4 5 6 Measurement position x mm Fig. 6. Experimental result. 4. Experimental results and discussion nother angle sensor for evaluation of the sensor sensitivity against the measurement position is fabricated based on simulation results. To minimize the influence of the beam spreading, the mm aperture is consisted before the objective lens. Fig. 6 shows the experimental results of sensor sensitivity ab each direction. The average sensor sensitivity and the deviation are 3.9 %/arc-seconds and.97 % in Δθ direction, and 3.6 %/arcseconds and. % in Δθ Z direction, respectively. The repeatability of this experiment is ab %, so the deviation V am_d is reduced as same level as repeatability. 5. Conclusion The relationship between the sensor sensitivity and measurement point of the mirror is analyzed and discussed based on Gaussian beam propagation. The geometrical analysis and simulation result indicate that the influence of the beam spreading becomes smaller by large initial beam diameter. nd the defocus amount x plays a roll for increasing / decreasing the sensor sensitivity. The design tolerance for positioning the QP is also estimated by using the parameter x. Then another angle sensor is fabricated based on simulation results. From the experimental result, the deviation V am_d is reduced up to %. 6. cknowledgements This research is financially supported by Grant-in-id for JSPS Fellows. References..E. Ennos and M.S. Virdee. High accuracy profile measurement of quasi-conical mirror surfaces by laser autocollimation. Precision Engineering. 98, 4(), pp. 5-8... Saito, W. Gao, and S. Kiyono. Single Lens-Micro ngle Sensor. International Journal of Precision Engineering and Manufacturing. 7,, pp. 4-9. 3. W. Gao, P. S. Huang, T. amada and S. Kiyono. compact and sensitive twodimensional angle probe for flatness measurement of large silicon wafers. Precision Engineering., 6, pp. 396-44. 4. H. Urey. Spot size, depth-of-focus, and diffraction ring intensity formulas for truncated Gaussian beams. pplied Optics. 4, 43(3). -