X-ray Interferometer of Separate Components | SPring-8/SACLA Research Frontiers

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X-ray Interferometer of Separate Components In the hard X-ray region most optical elements, s u c h a s m o n o c h r o m a t o r s , p o l a r i z e r s , c o l l i m a t o r s a n d b e a m e x p a n d e r s , a r e d e s i g n e d b a s e d o n d y n a m i c a l d i f f r a c t i o n w i t h p e r f e c t c r y s t a l s . In te rf er om et er s, on e of th e mo st im po rt an t op ti ca l e l e m e n t s , a r e a l s o m a d e o f p e r f e c t c r y s t a l s . F o r e x a m p l e , a s k e w - s y m m e t r i c t r i p l e - L a u e in te rf er om et er , wh ic h is an X- ra y an al og ue of th e Mach-Zehnder interferometer, has four thin blades making Laue case diffractions ( Fig. 1(a) ). First one acts as a beam splitter dividing the incident beam into two coherent beams. Two mirrors change the propagating directions of the two beams, and they m e e t o n t h e l a s t b l a d e . T h e l a s t b l a d e i s a r e c o m b i n a t o r , u s u a l l y t e r m e d a n a n a l y z e r , t h e p e r i o d i c e l e c t r o n d e n s i t y o f w h i c h a n a l y z e s a st an di ng wa ve ma de by th e in te rf er en ce be tw ee n t h e t w o b e a m s a n d y i e l d s M o i r e f r i n g e s . T h e spacing of the raw interference fringes is too small to be perceived directly due to the angstrom scale o f t h e w a v e l e n g t h . S o w e c a n c o n c l u d e t h a t w e need to achieve an angstrom scale stability for the o p e r a t i o n o f X - r a y i n t e r f e r o m e t e r s , o t h e r w i s e t h e interference fringes will be smeared out. This is the r e a s o n w h y m o s t X - r a y i n t e r f e r o m e t e r s a r e constructed on a single block of perfect crystal. However we may need a separate component i n t e r f e r o m e t e r , w h i c h i s m o r e f l e x i b l e a n d h a s a greater potential than the monolithic interferometer. For example, we can have a larger separation, say 1000 m, when the skew-symmetric interferometer is m a d e f r o m s e p a r a t e c o m p o n e n t s . ( N o t e t h a t t h e t w o c o h e r e n t b e a m s p r o p a g a t e p a r a l l e l t o e a c h o t h e r i n s i d e t h e i n t e r f e r o m e t e r . ) U s i n g a l a r g e s k e w - s y m m e t r i c b i c r y s t a l i n t e r f e r o m e t e r , w e a r e planning to detect the red-shift of X-rays due to the gravitational field of the earth in the 1-km-beamline BL29XUL [1]. Up to date, the separate component i n t e r f e r o m e t e r s h a v e b e e n r e a l i z e d o n a c o n v e n t i o n a l s t a t i c m e t h o d , w h e r e t h e i n t e r f e r e n c e i n t e n s i t y o s c i l l a t i o n w a s m e a s u r e d b y s c a n n i n g a p h a s e p l a t e o r t h e i m a g e o f i n t e r f e r e n c e f r i n g e s w e r e t a k e n a f t e r t h e s e p a r a t e c o m p o n e n t s w e r e e x t r e m e l y s t a b i l i z e d a s i f t h e r e w e r e m a d e o f a single crystal block. One big pro ble m on the sep ara te com pon ent i n t e r f e r o m e t e r s i s t h e s t r i n g e n t r e q u i r e m e n t o f stability, which is estimated to be less than 10 -10 m fo r tr an sl at io n an d/ or 10 -1 0 ra di an fo r an gl e. Th e conventional approach to the separate component i n t e r f e r o m e t e r s i s s u i t a b l e f o r a p h a s e s e n s i t i v e a p p l i c a t i o n s , s u c h a s p h a s e c o n t r a s t i m a g i n g , b e c a u s e t h e e f f e c t o f i n s t a b i l i t y o n p h a s e i n f o r m a t i o n i s r e l a t i v e l y s m a l l e r . H o w e v e r , t h e c o n v e n t i o n a l s t a t i c m e t h o d c a n n o t b e a p p l i e d t o v i s i b i l i t y s e n s i t i v e a p p l i c a t i o n s . T h e v i s i b i l i t y i s subject to degradation by residual instability of the interferometer, so that the measured value may be l o w e r t h a n t h e t r u e v a l u e . W e n e e d t o c o m p a r e t h e i n t r i n s i c v a l u e s o f v i s i b i l i t y m e a s u r e d u n d e r d i f f e r e n t c o n d i t i o n s o f c o m p o n e n t s , e . g . , c o h e r e n c e m e a s u r e m e n t s b y Y o u n g o r M i c h e l s o n i n t e r f e r o m e t e r s . Here we consider a new interferometric method to measure visibility [3]. Using this method, we can measure directly the intrinsic value of visibility and d o n o t n e e d t o s t a b i l i z e t h e i n t e r f e r o m e t e r . T h e principle is easy but somewhat tricky. We suppose th e ou tp ut in te ns it y of th e in te rf er om et er ch an ge s l i k e I ( φ ) = ( 1 + V c o s ( φ ) ) , w h e r e i s t h e a v e r a g e i n t e n s i t y , V i s t h e v i s i b i l i t y , a n d φ i s t h e p h a s e v a r i a b l e w h i c h i s r e l a t e d t o r e l a t i v e t r a n s l a t i o n a l a n d / o r a n g u l a r s h i f t s a m o n g t h e c o m p o n e n t s . S i n c e φ i s r e l a t e d t o t h e a n g s t r o m scale, it varies rapidly due to mechanical vibration a n d t h e r m a l d r i f t , i f s p e c i a l c a r e i s n o t t a k e n t o s t a b i l i z e t h e i n t e r f e r o m e t e r . W h e n i n t e n s i t y correlation is measured, it will be averaged over φ 93 a n d b e c o m e = 2 ( 1 + V 2 / 2 ) . T h u s t h e visibility is determined from the intensity correlation. W e h a v e i n v e s t i g a t e d t h e r e l a t i o n b e t w e e n visibility and the intensity correlation using a skew- s y m m e t r i c b i c r y s t a l i n t e r f e r o m e t e r . F i g u r e 1 ( b ) shows a schematic view of the experimental setup a t B L 2 9 X U L [ 2 ] . T h i s b i c r y s t a l i n t e r f e r o m e t e r consists of two separate Si blocks, one mounted on the splitter and the mirror-1, and the other mounted on the mirror-2 and the analyzer. The separation of t h e t w o b l o c k s w a s 5 0 0 m m . W e m e a s u r e d t h e i n t e n s i t y c o r r e l a t i o n o f t h e o u t p u t b e a m w i t h t w o avalanche photo diodes ( APD ) using a coincidence t e c h n i q u e . T o v e r i f y i n t e r f e r e n c e , w e a l s o monitored the beam image by a CCD based beam monitor (not shown in Fig.1(b) ). F i g u r e 2 s h o w s t h e t w o d i m e n s i o n a l m a p o f n o r m a l i z e d c o i n c i d e n c e m e a s u r e d i n t h e ∆θ 1 - ∆θ 2 plane. Here, ∆ θ 1 and ∆ θ 2 represent rotation angles wit hi n the sca tte rin g pl an es of ea ch cry sta l bl oc k. The coincidence rate was found to have a narrow peak along ∆ θ 1 = ∆ θ 2 line. This suggests that only the narrow region where the two blocks are nearly parallel can be used for interferometry. Note that t h e t w o c r y s t a l b l o c k s a r e e x a c t l y p a r a l l e l o n t h e ∆ θ 1 = ∆ θ 2 line, as if the interferometer is made of a s i n g l e c r y s t a l b l o c k . T h e r e a s o n w h y t h e c o i n c i d e n c e w a s e n h a n c e d w i t h t h e n a r r o w r a n g e a l o n g ∆ θ 1 = ∆ θ 2 w a s d i s c u s s e d i n R e f . [ 4 ] . T h e b e a m images taken along the constant- ∆θ 1 line ( ∆θ 1 =0.5”) s h o w c l e a r l y t h a t t h e i n t e r f e r e n c e f r i n g e s w e r e o b s e r v e d w i t h i n t h e s a m e r e g i o n w h e r e t h e Fig. 1. (a) Schematic view of a skew-symmetric triple Laue interferometer, which is an optical X-ray of Mach-Zehnder interferometer. Laue case diffractions take place at the four thin blades, splitter, two mirrors, and analyzer ( recombinator ). (b) Schematic side view of the experimental setup. The interferometer consists of two Si crystals separated by 500 mm. The output intensity was monitored by two APD detectors in transmission geometry, which were connected to the coincidence circuit to measure the intensity correlation. 94 Fig. 2. Two-dimensional map of the normalized coincidence, and the b e a m i m a g e s t a k e n a l o n g t h e c o n s t a n t - ∆ θ 1 l i n e ( r e d l i n e ) . T h e normalized coincidence had a sharp peak along ∆θ 1 = ∆θ 2 line, where the interference fringes were observed clearly in the beam images. c o i n c i d e n c e h a d a p e a k ( F i g . 2 ( b ) ) . T h u s t h e t h e o r e t i c a l r e l a t i o n , ~ 1 + V 2 / 2 , w a s c o n f i r m e d semiquantitatively. We ove rvi ewe d bri efl y the int erf ero met ry wit h s e p a r a t e c o m p o n e n t s a n d i n t e n s i t y c o r r e l a t i o n , u s i n g t h e s k e w - s y m m e t r i c i n t e r f e r o m e t e r . T h e i n t e n s i t y c o r r e l a t i o n t e c h n i q u e w a s f o u n d t o b e a g o o d m e a s u r e o f v i s i b i l i t y a n d m a y b e u s e f u l i n v i s i b i l i t y s e n s i t i v e a p p l i c a t i o n s b y s e p a r a t e c o m p o n e n t i n t e r f e r o m e t e r s , s u c h a s Y o u n g o r Michelson interferometers. Kenji Tamasaku RIKEN / SPring-8 E-mail: tamasaku @ postman.riken.go.jp References [1] T. Ishikawa et al. , Proc. SPIE 4145 (2000) 1. [ 2 ] K . T a m a s a k u , Y . T a n a k a , M . Y a b a s h i , H . Y a m a z a k i , N . K a w a m u r a , M . S u z u k i a n d T . Ishikawa, Nucl. Instrum. Meth. A 467-468 (2001) 686. [3] M. Yabashi et al. , Jpn. J. Appl. Phys. 40 (2001) L646. [ 4 ] K . T a m a s a k u , M . Y a b a s h i a n d T . I s h i k a w a , Phys. Rev. Lett. 88 (2002) 044801. -2 -1 0 1 1 0 -1 -2 1.0 1.5 ∆θ 1 (arcsec) ∆θ 2 (arcsec) 95