International Journal of Infrared and Millimeter Waves, VoL 3, No. 3, 1982

LABORATORY-SCALE MIRRORS FOR SUBMILLIMETER WAVELENGTHS

Gerald F. Dionne

Lincoln Laboratory, Massachusetts Institute o f Technology Lexington, Massachusetts 02173

Received October 30, 1981

A machining procedure based on an elementary concept has been applied successfully to produce metal mirrors suitable for submillimeter wavelengths. Ninety-degree off-axis para- boloidal or ellipsoidal mirror sections may be cut from brass or aluminum by means of a series of predetermined increments on a conventional laboratory lathe. Paraboloidal mirrors with low f-numbers (f/2) made by this technique have been used with good results as part of the collecting optics of a submillimeter-wave heterodyne radiometer.

Key words: paraboloidal and e t l ipsoidal mirrors, reflecting surfaces , submil l imeter-wave opt ics .

Introduction

At submillimeter wavelengths (0.1 - i. 0 ram), transmiss- ion usually involves a quasi-optical approach that guides the radiation by means of mirrors or lenses. Gonventional coaxial cable and waveguides so prevalent with microwaves are useless at these wavelengths because of power loss and mechanical fabrication problems. Since power sources in this region have limited strength (on the order of roW), even lenses with their 30 to 50 percent attenuation factors are seldom used where high-reflectivity mirror surfaces can per- form the same function. As a result, many occasions arise where small, fast (-~f/2) mirrors tailored to a specific app- lication can be of considerable value to the experimentalist.

417

0195-9271/82/0500-0417503.00/0 �9 1982 Plenum Publishing Corporation

418 Dionne

U n f o r t u n a t e l y , mirrors with t h e s e low f-numbers are a lmos t u n a v a i l a b l e c o m m e r c i a l l y a t the p r e s e n t t ime . A unique me thod employ ing a mi l l ing m a c h i n e for shap ing me ta l mirror s e c t i o n s wi th c o n t o u r s a p p r o x i m a t e d to the d e s i r e d c u r v a t u r e was r e c e n t l y r e p o r t e d (1). This p a p e r is an e x p a n d e d v e r s - ion of an e a r l i e r b r ie f no te (2), and d e t a i l s the l a b o r a t o r y method (3) fo r making mirrors with e x a c t con tou r s tha t would o t h e r w i s e be d i f f i c u l t to a c q u i r e e v e n by more s o p h i s t i c a t e d techniques.

Fabrication Techniques

The fundamental principle of the fabrication technique is based on the fact that mirrors with conic section contours are surfaces of revolution, with focal lengths and apertures defined precisely by the coefficients of their geometric equations. Consequently, equally spaced points lying on a cross-section curve through the axis of the particular surface

BRASS / OR

ELLIPSE EQUATION :

x 2 y2

MIXER DIODE WITH CORNER-CUBE REFLECTOR

Figure i. Design schemes for digital machining of parabol- oidal and ellipsoidal mirrors using a lathe for the increment- al cutting.

Mirrors for Submillimeter Wavelengths 419

may be c o m p u t e d d i r e c t l y and a s e t of x - y c o o r d i n a t e s g e n - e r a t e d to be u s e d for m ach i n i ng the c o n t o u r in a s e r i e s of s t e p s . The c o n c e p t is i l l u s t r a t e d in Fig. I , whe re e x a m p l e s of a p a r a b o l o i d and e l l i p s o i d are g i v e n .

With a c y l i n d r i c a l p i e c e of b r a s s or a luminum (which may have e x c e s s m a t e r i a l from the co re a l r e a d y r emoved) , the d e s i r e d c o n t o u r of the mirror was m a c h i n e d in i n c r e m e n t s as l a rge as 0 . 5 mm on a l a t h e wi th p r e c i s i o n of 0 . 0 2 5 ram. The a b o v e numbers were d i c t a t e d by the g e n e r a l r u l e - o f - thumb tha t i n c r e m e n t s i z e s shou ld not e x c e e d the s h o r t e s t w a v e l e n g t h of the i n t e n d e d a p p l i c a t i o n (a l though it is qu i t e p o s s i b l e t ha t l a r g e r s t e p s may be u s e d if the s u b s e q u e n t smoo th ing o p e r a t i o n s a re c a r r i e d ou t with s u f f i c i e n t c a r e to p r e s e r v e the e x a c t n e s s of t he d e s i r e d c o n t o u r ) . Step s i z e s of one w a v e l e n g t h and o n e - h a l f w a v e l e n g t h were u s e d wi th e q u i v a l e n t r e s u l t s . Al though r equ i r ing ca re and p a t i e n c e of the o p e r a t o r in e x e c u t i n g as many as I00 s t e p s , the method is c a p a b l e of p roduc ing s e v e r a l 9 0 - d e g r e e o f f - a x i s s e c t i o n s from a s i ng l e c y l i n d r i c a l b l o c k . From the 1 4 - c m d i a m e t e r , 4 - c m th i c k b r a s s c y l i n d e r shown in Fig. 2, e igh t mirror s e c t - ions of 2 . 5 - c m a p e r t u r e and 5 - cm f o c a l l e n g t h were o b t a i n e d by s l i c i ng wi th a band saw.

With the work m a t e r i a l s t i l l ro t a t ing on the l a t h e , the s u r f a c e w a s s m o o t h e d by hand p o l i s h i n g wi th p r o g r e s s i v e l y f i n e r g r a d e s of s and ing c l o t h and p a p e r unt i l a l l t r a c e s of the m a c h i n e d r i dges were no l o n g e r v i s i b l e . F ina l l y , a j e w e l l e r ' s rouge p o l i s h i n g compound u s e d wi th a buf f ing w h e e l a t t a c h e d to a dr i l l p r e s s p r o v i d e d a s u i t a b l e s u r f a c e f i n i s h . This l a s t s t a g e p r o d u c e d b e t t e r r e s u l t s when ca r r i ed out on the i n d i v i d u a l p i e c e s r a t h e r t han on the c o m p l e t e c y l - inde r . A t y p i c a l mirror f i n i s h ( see Fig. 3) was found to be on the o rde r of 0 .1 bm by means of a s u r f a c e p r o f i l o m e t e r mea s u r e m e n t .

Experimental Results_

In one successful application, a paraboloidal mirror section was used to focus far-field radiation from a lO-cm diameter blackbody source onto a Schottky-barrier diode used as a mixer in a submillimeter-wave radiometry experi- ment (see Fig. 4). Since the beam of the paraboloidal ant- enna was filled by the blackbody up to a distance of 5 m, it was concluded that the beamwidth conformed to the theoret-

420 Dionne

Figure 2. Photograph of metal cylinder after completion of the step-by-step cutting (in 0.5 mm steps) of the precalcul- ated mirror surface. Core of the material was removed initially to reduce machine operating time.

Mirrors for Subminimeter Wavelengths 421

Figure 3. Photograph of f i n i s h e d f /2 and f /1 p a r a b o l o i d a l 9 0 - d e g r e e o f f - a x i s mirror s e c t i o n s ; l e f t , 5 - cm foca l d i s t a n c e wi th 2 . 5 - c m aper ture ; r ight , 2 . 5 - c m f o c a l d i s t a n c e and 2 . 5 - cm a p e r t u r e .

i ca l d i f f r a c t i o n wid th 7t/D ~ 1 /50 r a d i a n s , w h e r e -A is the w a v e l e n g t h (--~ 0 .5 mm) and D is the mirror ape r tu re (25 mm). With th i s beamwid th , the c a l c u l a t e d beam d i a m e t e r at 5 m (--'~5 A/D) matched the 10-cm diameter of the source (see Fig. 5), verifying that the accuracy of the mirror was suffic- ient for applications at one-half millimeter wavelength. With a precision metallized-glass mirror of similar dimens- ions used in the same application, the experimental results did not improve in comparison with those cited above.

422 Dionne

MERCURY-ARC L ~

M JET~-ET,~ SPACE CHAMBER WITH 77K CRYOPANELS

STEA

i : . ' . . . . . . . N2 DRY BOX " - ' ~ " ~ ~ ~ BLACK BODY CONTIN U UM

"~ ~ . - '. ". "" ".."1 CHOPPER

I"' i ', ' .).1".:,'.;;~" .-.~. ; I 2rid LO BEAMSPLITTER SWEEP GENERATOR

B - , O o . , '

GI

REFERENCE ~ ,~L ,i~'~... . . . . .

SCHOTTKY DIODE

3GHz I ~S - ~.S

<1 MHz BW

PLOTTER

FREQUENCY

Figure 4. Block diagram of two-stage heterodyne radiometer for detecting the 752-GHz 1-120 rotational line in a laboratory jet operating in a high-vacuum space chamber.

I 4 IMAGE REGION

/ I/PARABOLOIDAL DEFOCUSED

'--_L

R ~'a SCHOTTKY DIODE WITH CORNER-CUBE

REFLECTOR

Figure 5. Optical arrangement for mercury-arc blackbody, off-axis paraboloidal mirror section, and Schottky diode used in radiometer experiments. Beamwidth of paraboloidal ant- enna is filled by the blackbody source and conforms to the theoretical diffraction-limited conditions atN0.5 mm wave- length.

Mirrors for Submillimeter Wavelengths 423

Acknowledgmen t s

The au tho r is g ra t e fu l to R. C. Lewis , R. J. Kel ley, ~. F. F i t zge ra ld , and Dr. T-S. Chang for a s s i s t a n c e in the f a b r i c a t i o n of the mirrors , to C. D. Parker for he lp ing with the b l a c k b o d y r a d i a t i o n t e s t s , and to W. Nowel l for ca r ry - ing out the su r face p ro f i lomete r m e a s u r e m e n t s . This work was sponso red by the Depar tment of the Army. The U. S. Government a s s u m e s no r e s p o n s i b i l i t y for the in format ion p r e s e n t e d .

Reference s

i. N.R. Erickson, Appl. Opt. 18, 956 (1979).

2. G.F. Dionne, Rev. Sci. Instrum. 52, 308 (1981).

3. G.F. Dionne, Technical Report TR-588, Lincoln Labor- atory, M.I.T. (7 October 1981). AD-AI07898.