Microrelief measurements for white-light interferometer with adaptive algorithm interferogram processing

Transcription

1 Mcrorelef easureents for whte-lght nterferoeter wth adaptve algorth nterferogra processng Evgeny V Sysoev, Rodon V Kulkov Technologcal Desgn nsttute of Scentfc nstruent Engneerng (TD SE Sberan Branch of the Russan Acadey of Scences (SB RAS 41, Russkaya str, Novosbrsk, , Russa Tel: + 7 [383] Fax: +7 [383] E-al: evsl@alru Abstract The proble of reducng easureent errors of surface crorelef wth nonunfor scatterng propertes usng whte-lght nterferoeter was dscussed Adaptve algorth of thresholdng whch allows us to set optal threshold n every pont of easurng surface was proposed Applcaton of ths algorth of threshold choce allows ncreasng dynacal range of nterference detecton ore than n 10 tes The dependences of scannng nterferoeter resoluton on dfferentonal nterferogra thresholdng have been dscussed Keywords: Relef easureent, nterference, surface qualty nspecton, thresholdng 1 ntroducton The scannng nterferoeter of partally coherence lght s wdely used under noncontact easureents of surface relef n scence and ndustry [1, ] The easureents are based on regstraton of nterference of partally coherence lght As t s known the nterference of partally coherent lght s observed whle optcal paths dfference n reference and easureent ars does not exceed coherence length of lght source used [3] The condton of nterference exstence defnes layer n a easureent feld wth depth about coherence length [4] Mean part of ths layer concdes wth projecton of rror surface wthn a easureent fled that nstalled n nterferoeter reference ar ts poston s defned fro the condton of optcal paths equalty n reference and easureent nterferoeter ars The dfferentonal nterferogras are used to extract nterference They are fored by subtracton of CCD regstered nterferogras shfted by phase Measureent of whole surface profle s perfored by depth scannng of easurng surface The scannng s realed by seral changng of nterferoeter poston relatve to easureent object wth the gven step se For nterference detecton, as a rule, fxed threshold s used [5] However, scatterng propertes of easurng surface can be sgnfcantly changed wthn the easureent feld, for exaple, under the fuel eleent surface easureents [6] n ths case, the use of fxed threshold akes dffcult nterference detecton n the felds, where apltude of scattered lght s too sall We have studed probles of easureent for crorelef surface wth nonunfor scatterng propertes Adaptve algorth for thresholdng that allows decreasng the easureent errors was proposed The dependence of scannng nterferoeter resoluton fro used apltude threshold was consdered The nfluence of threshold value on qualty factor Q defned as raton of a nuber of reconstructon ponts to total ones wthn easureent feld was deonstrated The algorth ncreasng qualty factor Q was proposed The easureent prncple Setup for experental nvestgatons of the ethod was assebled Fgure 1 shows ths setup 1-157

2 1 5 О О1 О 7 9 Fg 1 Schee of experental setup: 1 nterferoeter, CCD caera, 3 peoceracs controller, 4 coputer, 5 source of partally coherent lght, 6 beaspltter, 7 reference rror, 8 easured object, О1, О, О3 objectves, 9 peoceracs t ncludes nterferoeter 1, CCD caera, peoceracs controller 3 and coputer 4 nterferoeter conssts of source of partally coherent lght 5 wth effectve wavelength 065 and coherence length l c 1 8 µ, beaspltter 6, reference rror 7, objectves О1, О, О3 and easured object 8 Reference rror 7 of nterferoeter s nstalled on peoceracs 9 The optcal path length n the reference ar of the nterferoeter s adjusted by peoceracs voltage eoceracs was connected to controller 3 A halogen lap serves as source of partally coherent lght 5 Coputer 4 controls the step and range of rror dsplaceent The nterferogras were regstered by CCD caera then transtted to coputer A scannng on the depth of easured surface was carred out by eans of ovng of nterferoeter 1 wth step along optcal axs Two nterferogras were regstered on every step of scannng, one of whch was shfted by hase shftng was realed by rror 7 poston changng by eans of peoceracs 9 voltage changng Dfferentonal nterferogra (D s calculated as a result of absolute value after orgnal nterferogras subtracton The experents were carred out wth scannng steps 0 5 and1 Typcal dstrbuton of ntensty n whte-lght nterferoeter can be presented n the followng for: ( 4 (, 0 1 exp cos (, (1 lc where 0 s average value of ntensty, s optcal path dfference between reference and easurable ars, { } s set of nterferoeter postons, and s scannng step nuber Typcal vew of real nterferogra, whch s descrbed n (1, s shown n Fg (a For nterference extracton, D shown n Fg (b s used D s descrbed by the followng for: J(, (, (, ( 4 n experents a scannng was produced wth a step lc The set of values of ntensty J ( } was regstered n every pont of easurng surface Fnally, the absolute { value of poston Z, every eleent ( of easurng surface s defned by forula: l

3 where l (a (b Fg Real nterference sgna (a ntal nterferogra, (b dfferental nterferogra Z nl, 1, (3 nl, n, s nuber of D ntensty values regstered n pont ( of surface for dfferent, and for whch J( 0, where s threshold of nterference extracton Nose value n the regsterng nterferogras depends on ntensty and ts apltude s defned by the dsperson ~ Dfferentonal nterferogras thresholdng s used for nterference detecton aganst a background of nose The agntude of optal threshold value at sall dfference of ntensty on CCD atrx for easurng apltude value of dfferentonal nterferogra s defned by axu nose value Ths threshold s used for all ponts of easureent area Thus, ax, where ~, ax ax ax s axu ntensty of easureent feld f scatterng propertes of surface n easureent feld have sgnfcant dfferences, then, n CCD atrx sghts where ntensty saller than ax, applcaton of thresholdng leads to the fact that nterference for such surface regons wll not regstered To obtan the set { J( 0 } correspondng to a { } the scannng of parallel-sded plate has been done nterference s regstered not n all surface ponts of easurng area n ths case: ( Z Z k 1, (4 where s dsperson of Z and t defnes resoluton of surface profle easureent, s the nuber of ponts an nterference was regstered The results of experents of dependence on easured at scannng parallel-sded plate are presented n Fg 3(а (a (b Fg 3 (a Rs dependence on threshold and (b qualty factor dependence on threshold 1-159

4 The relable detecton of nterference on a background of nose s carred out by thresholdng, whch concludes n the choce of optu value of threshold Dependences Q on for dfferent scannng steps are presented n Fg 3 (b Fro ths fgure evdently, that for every value of scannng step there s a value of for whch the coeffcent Q begns strongly to dnsh Thus, for a recept axal Q, as s seen fro Fg 3 (b, t s necessary to choose a nu threshold f scatterng propertes of surface n the easurng area have nsgnfcant llunaton overfalls of CCD atrx, then an optu threshold s ax To decde ths proble the followng ethod was proposed Ths ethod allows us to set relatve threshold dentcal for every ponts of easurng surface n every scannng step t conssts of the followng For a D obtanng t s necessary to regster two nterferogras one of whch was shfted by For the calculaton of adaptve threshold at every atrx of correcton coeffcents s calculated: ~ ~, (5 ax( ~ (, 4 where l,, are nterferogras one of whch was shfted by phase on at every 4 Value ~ ~ does not contan nterference and s a total dstrbuton of brghtness n the ~ age of easured surface under scannng step Then adaptve threshold for every pont of easureent s calculated by forula: ~ (6 ~ ~ Snce ~ ax, then fro expressons (5, (6 one can obtan that ~ f l, ax dynacal range of nterference detecton s deterned as D f ax, then under ax ~ adaptve threshold a dynacal range wll be Da ~, where ( n s nal ( l, n ~ regstered ntensty level Under the use of CCD caera, the value ( s equal to 1, hence, D equals to D a f n For exaple, for 10-bt CCD caera the dynacal range of nterference detecton s ncreased n tes Applcaton of expresson (6 under nterferogras processng allows us substantally to proote easurng qualty of surfaces relef The grayscale age of easured surface, whch s resulted on CCD caera (see Fg 1 s shown n Fg 4 (a Fro Fg 4 (a t s seen that scatterng propertes of surface are hghly dffered Reconstructed 3D relefs wthout adaptve algorth usage and wth ts usage are shown n Fgs 4 (b, (c correspondngly As seen fro Fg 4 (b, easureent of surface relef wth threshold fxed for all ponts leads to large nuber of blanks n the easured relef t takes place because of nterference apltude for a any regons of easured surface s lower than fxed threshold and, thus, nterference s not regstrated Applcaton of the proposed algorth results n the substantal 1-160

5 proveent of easureents qualty Qualty factor Q n a frst case equals to 07, and n a second case s equal to 096 (a (b (c Fg 4 Experental results, (a grayscale age of easured feld, (b 3D surface relef easurng wthout adaptve algorth usage, (c 3D surface relef easurng wth adaptve algorth usage Measureent results of 3D surface relef wth usage of adaptve algorth s shown n Fg 4 (c Fro ths fgure t s seen that nuber of blanks have becae sgnfcantly saller 3 Concluson We have dscussed the proble of reducng easureent errors for surface crorelef wth nonunfor scatterng propertes n the whte-lght nterferoeter Adaptve algorth of nterferogras thresholdng for easureent qualty proveent of surface profle was proposed We have shown experentally that adaptve algorth of threshold choce allows one to ncrease dynacal range of nterference detecton ore than n 10 tes Due to an estaton of surface scatterng propertes under surface crorelef easureents wth adaptve algorth one can copletely autoate the easureent process Results of present work can be used for developent prograatcally algorthc software of nterference profle-eters for precson easureents 4 Acknowledgents Authors would lke to thank Dr Anatoly K otashnkov for valuable contrbuton and helpful dscussons References 1 de Groot, J Begen, J Clack, XC de Lega, and D Grgg Optcal nterferoetry for easureent of the geoetrc densons of ndustral parts Appl Opt 00, 19, pp M Davdson, K Kaufan, and Maor The coherence probe croscope Sold State Technol 1987, 30, pp M Born, E Wolf Osnov optk M: Nauka 1970 (n Russan 4 V Golubev, EV Sysoev, YuV Chugu erene poverhnostnh defektov na osnove nkokogerntno nterferoetr Datchk sste 1999, No 6, pp 5-30 (n Russan 5 Claus Rchter, Bernhard Wesner, Renhard Gro, Gerd Häusler Whte-lght nterferoetry wth hgher accuracy and ore speed Frnge 005 The 5-th nternatonal Workshop on Autoatc rocessng of Frnge atterns pp EV Sysoev, V Golubev, YuV Chugu, and VA Shakhatov Measureent of local devatons of a surface profle based on partally coherent lght nterference Optoelectroncs, nstruentaton and Data rocessng 004, vol 40, No 5, pp