Profile Measurement of Large Aspheric Optical Surface by Scanning Deflectometry with Rotatable Optical Devices - Error Analysis and Pre-experiment-

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1 Key Engineering Materials Vols (010) pp (010) Trans Teh Publiations, Switzerland doi:10.408/ Proile Measurement o Large Aspheri Optial Surae by Sanning Deletometry with Rotatable Optial Devies - Error Analysis and Pre-experiment- Muzheng Xiao 1,a, Satomi Jujo 1, Satoru Takahashi 1, Kiyoshi Takamasu 1,b 1 The University o Tokyo, Department o Preision Engineering Hongo 7-3-1, Bunkyo-ku, Tokyo , JAPAN a xiaomuzheng@nanolab.t.u-tokyo.a.jp, b takamasu@pe.t.u-tokyo.a.jp Keywords: Proile measurement, aspheri surae, sanning deletometry, autoollimator, error analysis, Pre-experiment. Abstrat Large aspheri mirrors with diameter over 300 millimeters with high surae auray are wildly used in many areas suh as astronomial telesopes. Intererometers are widely used in proile measurement o optial lat and sphere. However, standard reerene aspheri surae whih is neessary or this method is diiult to make. Sanning deletometry based on ESAD (Extended Shear Angle Dierene) is used to measure ultra-preise large near-lat and slight urved optial surae with the auray o sub-nanometer. However, it is not possible or it to measure aspheri surae beause o the limitation o the measuring range o autoollimators. We proposed a new measuring method to san the surae o a large aspheri optial surae using autoollimator with rotatable optial devies ixed on linear motion stage. To eliminate the inluene o the pithing error o the sanning stage, we use two mirrors releting laser omes rom autoollimator, whih have the same eet with a pentaprism used in ESAD. To enlarge the measuring range o the autoollimator, we use a rotatable mirror to it the hanges o the slope o the mirror surae under measurement. The error analysis o the method is done. Measurement o an optial lat mirror and a sphere mirror with diameter o 50 mm and biggest slope o 6000 ar-seond are done. The rotatable optial devies that we designed are proved eetive on eliminating the pithing error o the moving stage. 1. Introdution Aspheri mirrors and lenses are used more popular in optial industry beause they an improve orretion o aberrations [1]. These aspheri suraes are beoming more preise, and sale o them beomes to be larger than hundreds o millimeters. So, proile measurement o large aspheri surae beomes an important subjet. However, there is no measurement mahine that an measure an aspheri surae with diameter o hundreds o millimeters and with slope over 10 ar-degrees with preision o 10 nm. Intererometers have high eiieny when measuring optial suraes. However it aes diiulties when the aspheri surae has a large departure o slope rom the best itting reerene surae. Multi-probe method has low eiieny but an easily enlarge the horizontal measuring range. However, the problem o dierene between sensors is remained unsolved or multi-probe method. Sanning deletometary based on ESAD (Extended Shear Angle Dierene) is used to measure ultra-preise near-lat and slight urved optial surae with the auray o sub-nanometer []. However, this method annot measure suraes with large slope that is larger than the measuring range o the autoollimator. We proposed a new method using a rotatable mirror and a ixed mirror instead o the pentaprism in ESAD. The measuring range is enlarged and the pithing error o the sanning stage an also be

2 Key Engineering Materials Vols eliminated by the ixed mirror and rotatable mirror. Error analysis is done, experimental devies are designed and the pre-experiment is done.. Priniple The priniple o the method is shown as Fig. 1. Mirror under measurement is ixed. One rotatable mirror and one ixed mirror are assembled with moving stage. Laser ome rom autoollimator is releted twie by these two mirrors and then releted by the onave mirror under measurement. Ater releting by those two mirrors on the moving stage, laser goes bak to the autoollimator. Then the reletion angle o the onave surae is measured by autoollimator. The moving stage moves to san the whole surae o the onave mirror. And when the reletion angle beomes lose to the measuring range o the autoollimator, the rotatable mirror turns a ertain angle to it the slope o the onave mirror and ontinue sanning. The angle o the onave mirror on the line paralleled with the moving stage is known by sanning one. Then turn a ertain angle o the onave mirror revolving around the prinipal axis o the onave mirror and ontinue to san. The angle data measured by autoollimator is transormed to derivation, and then the proile data o the onave mirror is known by the ormals written as Eq. (1). 0 0 h (1) 1 i i i i 1 i 0,1,, n 1 Where i is the plaement o point i on the onave mirror. ' i means the derivation o point i. Fig. 1 Angle measurement system with one rotatable mirror and one ixed mirror 3. Error analysis Beore the Pre-experiment, error analysis is done to hek what kind o ators aet the measurement result and how they do it. The angle error is aused by error o autoollimator E s and the error aused by the oset o measuring point o the mirror under measurement Δx whih is deined as E x. There is no dierene between measuring spherial surae and aspheri surae by the method we proposed, we take spherial surae example or error analysis. The untion o the spherial surae is deined as Eq. (). And the seond derivative is alulated as Eq. (3). R x () R (3) 3 R x

3 606 Preision Engineering When x =0, E x = Δx / R. Beause E s and E x is independent and both o them is supposed to be random error, they are ombined as E shown as Eq. (4). E E E (4) s x The unertainty o proile measured by this method is N he hle (5) Where N is number o sampling data, h is sampling interval and L is the length o the mirror under measurement [3]. For example, i unertainty o autoollimator is 0.1 ar-seond (about 0.5 μrad), the position auray o sanning stage Δx is 1μm, the length o the mirror is 300 mm, the sampling interval h is 0.5 mm, R is 1000 mm, the unertainty o proile will be about 10 nm. The result o the error analysis shows that the method we proposed an get high preision o dozens o nanometers when the error ators are ontrolled well. 4. Pre-experiment 4.1 Pre-experiment devies Pre-experiments are done to veriy the method we proposed. As the pithing angle o sanning stage will aet the angle data o the mirror, the pithing and yawing data is measured by an autoollimator beore measuring the proile o mirrors. Photograph o pre-experiment is shown in Fig.. Parameters o key devies are shown in Table 1. Fig. Experimental set up or proile measurement Table 1 Parameter o key devie or pre-experiment Name o the devie Moving/measuring rage Repeatability Resolution Autoollimator 00 ar-seond unknown 0.01 ar-seond Linear stage 35 mm 3 μm 5 nm Rotatable stage 360 degree 0.0 degree 0.5 ar-seond

4 Key Engineering Materials Vols Proile measurement o lat mirror The pithing data is measured or our times by autoollimator shown in Fig. 3. The data o pithing angle an be used to ompensate the measurement data o mirrors. A lat mirror with diameter o 50 mm is measured by sanning in one line. The moving range o the sanning stage is 35 mm, so only part o the mirror is measured. Beause the latness o the mirror is small, the eet by pithing o sanning stage is large. The proile data ompensated with the angle data o sanning stage is shown in Fig. 4(a). Fig. 3 Pithing data o sanning stage To eliminate the eet o pithing angle o sanning stage, another mirror is set on the sanning stage to make one more time reletion o laser rom autoollimator (shown as Fig. (b)). These two mirrors together have the same eet with a pentaprism. Proile o lat mirror is shown in Fig. 4 (b). The result shows that data measured by two-mirrors-releting is better than that by one mirror releting. Fig. 4 Proile data o lat mirror: (a) by one releting mirror, (b) two releting mirrors 4.3 Proile measurement o onave mirror Conave mirror with diameter o 50 mm and with urvature radium o 5000 mm is measured as the priniple shown in Fig.1. Measurement is done or 6 times. Data is shown in Fig. 5 (a). Beause the angle data is not ontinuous, we onnet the angle data. The measure point ater eah rotation o rotatable mirror is onsidered to be the same point beore rotation. In other words, the lost part aused by rotation is not onsidered. And the onneted data is shown in Fig. 5 (b). Fig. 5 (a)angle data o onave mirror (b) Conneted angle data o onave mirror

5 608 Preision Engineering Then the onneted angle data is used to alulate the proile data by Eq. 1. The proile data is shown as Fig. 6. Fig. 6 Proile data o onave mirror rom alulation o angle data 5. Conlusion A new method by sanning deletometry with rotatable optial devies or measuring aspheri method is proposed and the error analysis and pre-experiments are done. The system designed is proved that it an eliminate eet o pithing angle o sanning stage. Proile o onave mirror with slope o 500 ar-seond is measured by an autoollimator with measuring range o 00 ar-seond. The measuring range is proved to be enlarged by our new method. 6. Aknowledgement The present researh was supported partly by Global COE Program, Global Center o Exellene or Mehanial Systems Innovation, by the Ministry o Eduation, Culture, Sport, Siene and Tehnology o Japan. Reerene [1] Shulz, G., Aspheri suraes, in Progression Optis, E. Wol ed., vol. 5, , Elsevier Siene Publishers, [] Ral D. Gekeler, Ingol Weingaertner, Sub-nm topography measurement by deletometry: latness standard and waer nanotopography, Pro. SPIE, Vol. 4779, 1, 00. [3] GAO Wei, Nano-Metrology o Large Surae Proiles Using Angle Sensors, Journal o the Japan Soiety o Preision Engineering,,Vol. 68(3), pp , 00.