"longitudinal" gradients, where the temperature gradient is in the direction from the CMA to the

primary (parallel to the primary mirror axis of symmetry), and "transverse" gradients, which are

perpendicular to the longitudinal gradients. Both cases assume, as a worst-case scenario, that the

gradient direction lies in the plane of the optical bench.

For convenience, I summarize here the calculations that follow in Sections 2 and 3. I find that

the change in basic angle

due to the imposition of a gradient

is

dy

= -

2*a*

cos

2

x c

È

+

*O*

(

c

È

2

)

for the longitudinal case and

dy

=

2

*h*

+

*a *tan x

cos

2

x c

Ç

+

*O*

(

c

Ç

2

)

for the transverse case. Here,

, where

is the CTE of the material,

is the angle of the

c h a $ b

CMA mirrors with respect to the primary mirror symmetry axis,

*h* is the distance along the sym-

metry axis from the CMA support(s) to the CMA mirrors, and *2a* is the width of the CMA block

(same as the primary mirror width, currently 60 cm). (cf. Figures 1, 3, and 6.) These equations

impose the temperature gradient constraints

b

È

[

cos

2

x

2*a *a t

and

*Basic Angle Temperature Gradient Sensitivity*

*FTM-USNO-95-01*

2

5

10

15

20

25

30

35

40

45

50

1

1.5

2

2.5

3

3.5

4

4.5

5

14

13

12

11

10

10

9

9

8

8

7

7

6

6

5

5

5

4

4

4

3

3

3

2

2

1

1

Figure 2

(10

-8

K

-1

)

(mK/m)

(

µ

as)