Advanced optical metrology of geometrical quantity based on pulse trains destructive interference

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1 Advand optial metrology of geometrial quantity based on pulse trains destrutive interferen ODong WEI, Satoru TAKAHASHI, Kiyoshi TAKAMASU, and Hirokazu MATSUMOTO Department of Preision Engineering, The University of Tokyo # Corresponding Author / weidong@nanolab.t.u-tokyo.a.jp TEL: , FAX: KEYWODS : Ultrafast phenomena, Super-resolution, Coheren, Interferometry, Metrology The interferometri measurement using the femtoseond optial frequeny omb (FOFC) is in progress at present. We had analyzed the temporal oheren funtion of the FOFC sin it is the fundamental desription of interferen phenomenon. As a result, it had been understood that the oheren peak exists during the time whih is equal to the etitions interval in the traveling diretion of the FOFC. In order to make the best use of the temporal oheren harateristi, we propose a novel interferometri tehnique using an FOFC to observe the destrutive interferen between two pairs of pulse trains with different relative delays. Theoretial and simulation analysis of the FOFC shows that it offers a signifiantly different hallenge for length measurement. This tehnique an be applied not only to surfa profilometry and tomography, but also to optial super-high resolution metrology. Manusript reived: July 15, 2009 / Apted: August 15, 2009 NOMENCLATUE FOFC = femtoseond optial frequeny omb TCF = temporal oheren funtion 1. Introdution Measurements of lengths are strongly demanded for not only sien purposes but also industry requirements. Due to its inreased frequeny stability and very broad frequeny band, the femtoseond optial frequeny omb (FOFC) is a good hoi for high preision long-distan measurements. In 1998, Chekhovsky et al. suggested a possible sheme for a pulse distan-measuring interferometer using an FOFC as a low oheren light sour. [1] In 2000, Minoshima and Matsumoto measured the phase shift of the FOFC beat omponent between longitudinal modes for long distan measurements. [2] In 2001, Yasui et al. proposed a method that high temporal oheren of an unbaland optial-path Mihelson interferometer produd an adjant pair of pulse trains from an FOFC for length measurement to test stabilization of the FOFC light sour. [3] Following that pioneering work, various experiments were proposed using the high temporal oheren peak between a pair of pulse trains for length measurements. In 2002, Yamaoka et al. orted a new interferometry tehnique by using high temporal oheren of different pair of pulse trains from an FOFC to preisely alibrate the group refrative index of air for improving length measurements. [4] In 2004, Ye proposed to use high temporal oheren between a different pair of pulse trains from an FOFC for a long arbitrary length measurement to be less than an optial fringe by hanging the pulse etition frequeny of the FOFC. [5] In 2006, Ki-Nam Joo and Seung-Woo Kim orted a method that enables to measure the length between two onseutive pulse trains by observing the interferen fringes in frequeny domain. [6] In 2008, Cui et al. experimentally demonstrated a possible new sheme to apply the proposal of Ye, sanning the referen mirror of the unbaland optial-path Mihelson interferometer between the pulse etition periods of the FOFC to obtain the interferen fringes between different pairs of pulse train instead of hanging the pulse etition frequeny of the FOFC. [7] In 2009, A numerial model of pulse propagation in air was orted and was applied to length measurements by using interferen fringes between hirped pulses in short displaments by Balling et al. [8] and long displaments by Cui et al. [9]. enerally speaking, using only one FOFC light sour for a length measurement to be less than an optial fringe that means one must to observe the interferen fringes between pairs of pulse train. For a long arbitrary length measurement to be less than an optial fringe that means one must to observe the interferen fringes between pairs of pulse train in the range of the pulse etition periods of the FOFC as proposed by Ye to hange the pulse etition frequeny of the FOFC and as proposed by Cui et al. to san the referen mirror between the pulse etition periods of the FOFC. However, it is a trade-off relation between the variability and the stability of frequeny of the FOFC. And there is no simple devi whih an do sanning the range of the pulse etition periods of the FOFC suh as 30 m [7] to 6 m [2] with sub-nanometer resolution. Using two FOFC light sour potentially provide another solution. But to obtain the intermode beat [10] or the interferen fringes [11] between different pulse train from different FOFC light sours that means the following things of the two FOFC light sours. The very

2 good stability of phase loks and the differential frequeny between the pulse etition frequenies are required. The measurement system will beome expensive and ompliated. However, to obtain the interferen fringes between pairs of pulse train, the use of high temporal oheren in these experiments [1-9] is restrited to a pair of pulse trains. We have investigated the temporal oheren funtion of a pulse train from an FOFC. [12, 13] The results show that same high temporal oheren peaks exist during the period equal to the etition intervals in the traveling diretion of the FOFC. We have presented a novel interferometri tehnique using an FOFC to simultaneously observe separated high temporal oheren peak between two pairs of pulse trains with different relative delays [14-16]. As a speial demonstration, measurement of the average temperature hange over a distan of 3 m was also demonstrated. [14] Based on these previous works, in this study, we demonstrated a modified Mihelson interferometer to simultaneously observe overlapped high temporal oheren between different pairs of pulse trains from an FOFC for a long length measurement to less than an optial fringe. This is, to the best of our knowledge, the first demonstration of simultaneous observation of overlapped high temporal oheren peaks between two pairs of pulse trains with different relative delays. From a different perspetive, our results show that this tehnique an be used as diret link between the FOFC and length measurement. Fortunately, this new approah to highauray length metrology, by ombining an ordinary Mihelson interferometer and an unbaland optial-path reversed-phase interferometer, has its own advantages. First, as shown below, this tehnique maintains the simpliity of the equipment. Seond, the displament metrology an be ahieved without fringe analysis whih typially restrited the measurement speed in an ordinary Mihelson interferometer sheme. For simpliity of explanation, we have negleted the dispersion and absorption of the optial devis The outline of this ort is as following: Setion 2 gives a review of priniples for the FOFC light sour, the TCF of the FOFC and interferen fringes formation between different pairs of pulse train, Setion 3 investigates simulation, and lastly Setion 4 presents a summary. 1 ( ) F A( f f ) omb( T ), omb( T ) ( mt ). m From Eq. (2), the temporal oheren funtion periodially displays a high temporal oheren peak where the pulse trains signal of the FOFC displays a high-intensity peak with the pulse etition period T. 2.3 Interferen fringes formation between two pairs of pulse train The optial omb mode-lok tehnique results in interferen fringes reappearing between different pairs of pulse trains. When one pulse train E and the relatively delayed pulse train E finally train1 train2 overlap in spa, one an expet that interferen fringes an be observed. After performing the time integration we obtain the interferen fringes as E () t train1 M 1 BS E () t train2 ht 2 (a) (2) It ( ) ( ) os[mod( h, 2 )]. (3) M 2 (i+3)th E () t train1 E () t train2 (i+2)th Fig. 1. elative delay between pulse trains formed by an unbaland optial-path Mihelson interferometer (a) Simplified optial layout for interferometry. (b) elative positions between two pulse trains (integer h=1) (b) (i+2)th (i+1)th (i+1)th (i)th t t 2. Priniples 2.1 An FOFC In the time domain, the arrier pulse moves with the nter arrier frequeny f of the FOFC. When the eletri field paket eats at the pulse etition period T s by to the arrier-envelope phase beause of the differen between the group and phase veloities. In the frequeny domain, a modeloked FOFC generates equidistant frequeny omb lines with the pulse etition frequeny f 1 T, and due to phase slip, the whole equidistant-frequeny omb is shifted by f. 2.2 TCF of an FOFC For onvenien of explanation, we herein briefly review and summarize the most important harateristi of the temporal oheren funtion of an FOFC, whih an be founded in derails in ef.[12] The power spetrum of an FOFC light sour an be expressed as P( f ) A( f f ) omb( f ), (1) omb( f ) ( f mf ), m where A( f f ) is the envelope funtion of the FOFC power spetrum. Based on the WienerKhinthine theorem, the interferometri signal of the autoorrelation funtion is given by the inverse Fourier transform of the spetrum of the sour, and we have CEO Fig. 2. Simplified optial layout for the proposed interferometry. Fig. 3. Interferen fringes formation with the different displaments.

3 (a) same diretion, but the slippage of the interferen fringe phase to the arrier-envelope between them is reversed (namely, ). The result is that the two interferen fringes ompletely anl eah other out when there is omplete overlap (see Fig.3(b)). At the state of omplete overlap, no interferen fringes an be observed at the BS. In the ase, that the two interferen fringes partly overlapped eah other, the amplitude of the obtained interferen fringes will be redud. (see Fig.3(a,)) In essential, by observing the relative peak value of the aquired interferen fringes, one an obtain the length information between two separated points. 3. Simulation (b) The simulation is arried out with a aussian profile polarization mode loked FOFC. The pulse duration, the etition rate of the FOFC are 180 femtoseonds and100 MHz, respetively. The output wavelength of the pulse is ntered at =1550 nm with a spetral width of = 80 nm. The orresponding oheren length is L = Figure 4 illustrates the aquired interferen fringes peaks formed for the surfa of M and M o1 and the surfa of M and M o2, respetively. As shown in Fig.4, we an onfirm the interferen fringe phase slip to the arrier-envelope between aquired interferen fringes. As noted in Fig.5, the peak formed for the surfas of M and M o2 omes lose to the peak formed for the surfa of M and M o1, by reduing the displament between the two mirrors M o1 and M o2, the maximum peak value of the aquired interferen fringes and the the sum of the surfa integral between the aquired interferen fringes and the x axis are periodially redud. When the two interferen fringes peaks ompletely overlapped, by reduing the relative delay displament between the two mirrors M o1 and M o2 equals to zero, the two interferen fringes anlled eah other out. Then the aquired interferen fringes value is zero. 4. Summary Fig. 4. Interferen fringes. (a) Between M and M o1. (b) Between M and M o Interferen fringes formation between three pairs of pulse train Let us onsider the interferen fringes formed by a modified Mihelson interferometer, as shown in Fig. 2. The pulse train from the FOFC is introdud into the modified Mihelson interferometer. The modified Mihelson interferometer is a ombination of an ordinary Mihelson interferometer and an unbaland optial-path reversed-phase Mihelson interferometer. The ordinary Mihelson interferometer is omposed of a beam splitter BS, a referen mirror M, and an objet mirror M o1. The unbaland optial-path reversed-phase Mihelson interferometer is omposed of the same BS and M, and a different objet mirror M o2 to vary the relative delay between the pulse trains, whih are refleted by the surfa of the mirror M o1. The mirror M o2 is loated far from the surfa of the M o1 at a distan of h T /2 m (where h. ) in spa. During the measurement, by moving the ommon referen mirror M of the two interferometers by means of a omputerontrolled and alibrated ultrasoni stepping motor SM, we observed the following interferen fringes. After traveling different path lengths, these two pulse trains overlap at the beam splitter. Lens L 1 images the interferen fringe pattern onto a photodetetor PD. In Fig. 3, the pairs of interferen fringe pattern, whih are respetively formed between the referen mirror M and the surfa of mirror M o1, and between the referen mirror M and the surfa of the mirror M o2, have the same value of amplitude and move in the We have presented a novel interferometri tehnique using an FOFC to observe the destrutive interferen between pairs of pulse trains with different relative delays for a length measurement. It is important to note that beause it was possible to simultaneously observe overlapped high temporal oheren between different pairs of pulse trains with the reversed-phase, the relative positions of two separated point ould be measured without fringe analysis. The results of this investigation show that, with an appropriate optial system, the FOFC an be used to observe the destrutive interferen for a length measurement. Finally, it is antiipated that the present tehnique will be a powerful metrologial tool not only for surfa profilometry and tomography but also for super-resolution metrology. ACKNOWLEDEMENTS Part of this researh work was supported by the lobal Center of University of Tokyo, from the Japanese overnment. We are also grateful to NEOAK Corporation for providing the femtoseond fiber laser. Dong Wei gratefully aknowledges the sholarship given from Takayama International Eduation Foundation, Heiwa Nakajima Foundation, Ministry of Eduation, Culture, Sports, Sien, and Tehnology of Japan, respetively.

4 Normalized intensity [arb. unit] Path differen [1 step= 26nm] Between M and M o1 Between M and M o2 A C B D E F H

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