TO: File FROM: Robert A. Arnold SUBJECT: Secondary Mirror Motion Travel Limits DATE: 23-January-1996 ----------------------------------------------------------------- =============== Table of Contents =============== I. IntroductionII. Maximum Travel For Each Basic Mirror Motion
III. Maximum Travel For Each Mirror Motion With Roll Optimization
IV. Maximum Travel For Each Mirror Motion With Focus Present
V. Maximum Travel For Each Mirror Motion With Both Focus and Lateral Translation Present
VI. Summary Of Maximum Travel For Each Mirror Motion Table 1. Maximum Secondary Mirror Motions And Actuator Steps Table 2. Maximum Secondary Mirror Motions And Actuator Steps When Roll Angle Is Optimized Table 3. Maximum Secondary Mirror Motions And Actuator Steps In The Presence Of A Plus 2.0 Millimeter Focus Motion Table 4. Maximum Secondary Mirror Motions And Actuator Steps In The Presence Of A Minus 2.0 Millimeter Focus Motion Table 5. Maximum Secondary Mirror Motions And Actuator Steps In The Presence Of A Plus 2.0 Millimeter Focus Motion And A Plus 2.0 Millimeter X Decenter Motion Table 6. Maximum Secondary Mirror Motions And Actuator Steps In The Presence Of A Plus 2.0 Millimeter Focus Motion And A Minus 2.0 Millimeter X Decenter Motion Table 7. Maximum Secondary Mirror Motions And Actuator Steps In The Presence Of A Plus 2.0 Millimeter Focus Motion And A Plus 2.0 Millimeter Y Decenter Motion Table 8. Maximum Secondary Mirror Motions And Actuator Steps In The Presence Of A Plus 2.0 Millimeter Focus Motion And A Minus 2.0 Millimeter Y Decenter Motion Table 9. Maximum Secondary Mirror Motions And Actuator Steps In The Presence Of A Minus 2.0 Millimeter Focus Motion And A Plus 2.0 Millimeter X Decenter Motion Table 10. Maximum Secondary Mirror Motions And Actuator Steps In The Presence Of A Minus 2.0 Millimeter Focus Motion And A Minus 2.0 Millimeter X Decenter Motion Table 11. Maximum Secondary Mirror Motions And Actuator Steps In The Presence Of A Minus 2.0 Millimeter Focus Motion And A Plus 2.0 Millimeter Y Decenter Motion Table 12. Maximum Secondary Mirror Motions And Actuator Steps In The Presence Of A Minus 2.0 Millimeter Focus Motion And A Minus 2.0 Millimeter Y Decenter Motion Table 13. Summary of Maximum Secondary Mirror Motions
A computer simulation study has been performed in order to evaluate the maximum available travel of the secondary mirror for each of six basic mirror motions. The six basic mirror motions selected for consideration in this study are: focus, roll, lateral translation (2), and tilt about the mirror vertex (2). This study has also included the evaluation of a number of selected combinations of these six mirror motions in order to quantify their interdependence. The computer program which was developed for the controlling of the secondary mirror actuators has been used in this study of the maximum travel achievable for each of the motions of interest.
The fundamental limitation on the maximum travel available for any given mirror motion is the finite travel of each of the six actuators which position the mirror relative to the assembly base. This study has been performed under the assumption that each of the actuators is limited to a maximum extension or retraction relative to the center position of 1,500 steps. Each actuator step is nominally two microns ( 80 micro-inches ) of motion. This same value is programmed into the computer program which is used to compute the combinations of actuator steps that are required to position the mirror at any given combination of translations and rotations relative to the centered position.
It is noted that the physical motion of the secondary mirror may also be limited by one or more mechanical constraints which are imposed by the structure into which the secondary mirror assembly is installed. These mechanical constraints have been assumed to be not applicable for the purposes of this study. In the event that such constraints are imposed by the structure, the maximum travel values presented in this study may not be achievable.
II. Maximum Travel For Each Basic Mirror Motion
The maximum obtainable travel relative to the centered position for each of the basic secondary mirror motions is presented in Table 1. This table includes data for motions in both directions of travel as the geometry of the secondary mirror mounting assembly changes slightly as the mirror moves. The number of steps for each actuator are also shown in Table 1 for information purposes. The motions of focus, X decenter and Y decenter are in units of microns and the motions of X tilt about the vertex, Y tilt about the vertex and roll are in units of arc-seconds.
Table 1. Maximum Secondary Mirror Motions And Actuator Steps
Motion Travel Act 1 Act 2 Act 3 Act 4 Act 5 Act 6
Focus +4285 -1500 -1500 -1500 -1500 -1500 -1500
-4198 1500 1500 1500 1500 1500 1500
X Dec +4823 -1451 40 1500 -1451 40 1500
-4823 1500 40 -1451 1500 40 -1451
Y Dec +4203 -716 1500 -716 -716 1500 -716
-4290 785 -1500 785 785 -1500 785
X Tilt +5363 -269 -1191 1500 1500 -1191 -269
Vertex -5446 326 1216 -1500 -1500 1216 326
Y Tilt +5189 -1498 -974 517 -488 1018 1500
Vertex -5189 1500 1018 -488 517 -974 -1498
Roll +7778 1500 -1483 1500 -1483 1500 -1483
-7778 -1483 1500 -1483 1500 -1483 1500
Units: Focus, X Decenter, Y Decenter: microns
X Tilt, Y Tilt, Roll: arc-seconds
As is shown in Table 1, for each basic motion, one or more of the actuators has reached the maximum travel of 1,500 steps. It is noted that the motion of the mirror motion which is a Y tilt about the vertex of the mirror is a clear candidate for using roll motion of the mirror to enable a significant increase in the amount of Y tilt motion obtainable. This opportunity will be explained in the next section of this report.
III. Maximum Travel For Each Mirror Motion With Roll
Optimization
Under certain conditions, the introduction of a measure of roll motion can allow further motion than is presented in Table 1. When one or more actuators are at the limit for the number of steps, an appropriate measure of roll may be able to back these actuators away from the limit and thereby allow further travel. The condition which must be satisfied for this roll motion to allow improvement is that the roll motion which gives relief to the actuator at the limit must not cause any other actuator to move beyond it's limit. This condition will not be satisfied if two actuators, where both are even numbered or both are odd numbered, are at opposite arithmetic sign step limits. This condition will also not be satisfied if two actuators, where one is even numbered and the other is odd numbered, are at the same arithmetic sign step limits.
Applying these conditions to the data in Table 1, it can be seen that most mirror motions can not be extended be the application of roll motion. For the case of focus motion, actuators 1 and 2 are both at the same arithmetic sign step limit for both directions of motion. For positive X decenter, actuators 3 and 6 are both at the same arithmetic sign step limit while for negative X decenter, actuators 1 and 4 are both at the same arithmetic sign step limit. For Y decenter, actuators 2 and 5 are both at the same arithmetic sign step limit for both directions of motion. For X tilt about the vertex, actuators 3 and 4 are both at the same arithmetic sign step limit for both directions of motion.
Only for the case of Y tilt about the vertex can a measure of roll motion allow further travel of the basic motion. This combination of motions is presented in Table 2. As can be seen in this table, the introduction of about one thousand five hundred arc-seconds of roll extends the maximum Y tilt travel by about one thousand arc-seconds, or by about twenty percent relative to the value obtainable without any roll motion.
Table 2. Maximum Secondary Mirror Motions And Actuator Steps
When Roll Angle Is Optimized
Motion Travel Act 1 Act 2 Act 3 Act 4 Act 5 Act 6
Y Tilt +6173 -1496 -1440 906 -860 1500 1500
& Roll +1487
Y Tilt -6173 1500 1500 -860 906 -1440 -1496
& Roll -1487
Units: Y Tilt, Roll: arc-seconds
It is noted that the computer program which was developed for controlling the actuators applies mirror motions one at a time. As a result, in order to achieve the maximum motion using roll angle optimization, the program inputs must alternate many times between the tilt angle input and the roll angle input. This procedure does settle into the maximum motion, but it also complicates moving away from that motion limit position. In order to move away from the motion limit, the sequence of alternating between tilt angle input and roll angle input must again be repeated equally as many times.
In response to this opportunity to realize greater maximum travel under certain circumstances, the roll orientation of the mirror will be optimized when beneficial to the study results.
IV. Maximum Travel For Each Mirror Motion With Focus
Present
The execution of motion in any one basic mirror motion will typically result in a reduction of the available travel for the remaining mirror motions. As the intended operating travel for the mirror is specified to be +/- 2.0 millimeters in both focus and lateral displacement ( simultaneously ), an assessment of the remaining travel available in the presence of a 2.0 millimeter ( 2,000 micron ) focus motion was performed. The results from this assessment are presented in Tables 3 and 4 for positive and negative 2.0 millimeter focus motions respectively.
It is noted that no specific requirement has been defined for the amount of tilt that shall be available under any of the possible focus or decenter displacement combinations.
Table 3. Maximum Secondary Mirror Motions And Actuator Steps In
The Presence Of A Plus 2.0 Millimeter Focus Motion
Motion Travel Act 1 Act 2 Act 3 Act 4 Act 5 Act 6
X Dec +2600 -1500 -693 106 -1500 693 106
-2600 106 -693 -1500 106 693 -1500
Y Dec +4645 -1500 971 -1500 -1500 971 -1500
-2243 -297 -1500 -297 -297 -1500 -297
X Tilt +3574 -882 -1500 288 288 -1500 -882
Vertex -2893 -543 -58 -1500 -1500 -58 -543
Y Tilt +2762 -1500 -1223 -429 -971 -173 92
Vertex -2762 92 -173 -971 -429 -1223 -1500
Roll +4123 97 -1500 97 -1500 97 -1500
-4123 -1500 97 -1500 97 -1500 97
Y Tilt +3346 -1500 -1500 -200 -1194 109 93
& Roll +870
Y Tilt -3346 93 109 -1194 -200 -1500 -1500
& Roll -870
Units: Focus, X Decenter, Y Decenter: microns
X Tilt, Y Tilt, Roll: arc-seconds
As can be seen in Table 3, the introduction of the optimized roll angle increased the maximum available travel in the Y tilt motion by approximately 21 percent.
Table 4. Maximum Secondary Mirror Motions And Actuator Steps In
The Presence Of A Minus 2.0 Millimeter Focus Motion
Motion Travel Act 1 Act 2 Act 3 Act 4 Act 5 Act 6
X Dec +2581 -64 722 1500 -64 722 1500
-2581 1500 722 -64 1500 722 -64
Y Dec +2243 326 1500 326 326 1500 326
-4351 1500 -795 1500 1500 -795 1500
X Tilt +2817 558 86 1500 1500 86 558
Vertex -3543 923 1500 -273 -273 1500 923
Y Tilt +2725 -77 189 975 455 1245 1500
Vertex -2725 1500 1245 455 975 189 -77
Roll +4141 1500 -73 1500 -73 1500 -73
-4141 -73 1500 -73 1500 -73 1500
Y Tilt +3248 -77 -62 1179 256 1500 1500
& Roll +797
Y Tilt -3248 1500 1500 256 1179 -62 -77
& Roll -797
Units: Focus, X Decenter, Y Decenter: microns
X Tilt, Y Tilt, Roll: arc-seconds
As can be seen in Table 4, the introduction of the optimized roll angle increased the maximum available travel in the Y tilt motion by approximately 19 percent.
As is shown in Tables 3 and 4, the actuator system is fully able to provide 2.0 millimeters lateral translation in any of the four directions simultaneously with 2.0 millimeters of focus motion.
V. Maximum Travel For Each Mirror Motion With Both Focus and
Lateral Translation Present
An issue of interest is the amount of mirror tilt that can still be obtained when both the focus and lateral decentration motions are at their 2.0 millimeter travel requirements. In order to explore this issue, a number of combinations of 2.0 millimeter focus motion and 2.0 millimeter decenter motion were evaluated to determine the magnitudes of the decenter and tilts that could be realized in the remaining degrees of freedom. The data for a focus motion of plus 2.0 millimeters combined with X and Y decentrations of plus and minus 2.0 millimeters is presented in Table 5 through Table 8. The data for a focus motion of minus 2.0 millimeters combined with X and Y decentrations of plus and minus 2.0 millimeters is presented in Table 9 through Table 12.
Table 5. Maximum Secondary Mirror Motions And Actuator Steps In
The Presence Of A Plus 2.0 Millimeter Focus Motion And
A Plus 2.0 Millimeter X Decenter Motion
Motion Travel Act 1 Act 2 Act 3 Act 4 Act 5 Act 6
Y Dec +1022 -1500 -332 -261 -1500 -332 -261
-2263 -903 -1500 326 -903 -1500 326
X Tilt +3605 -1499 -1500 911 -308 -1500 -260
Vertex -655 -1282 -551 -261 -1500 -551 -47
Y Tilt +633 -1500 -816 -19 -1378 -575 101
Vertex -4242 -95 113 -496 -899 -1500 -1305
Roll +954 -1134 -883 105 -1500 -514 -267
-945 -1500 -512 -267 -1137 -879 102
X Tilt -1628 -1500 -57 -803 -1500 -605 280
& Roll -1412
Y Tilt +951 -1500 -968 107 -1500 -422 100
& Roll +476
Y Tilt -4653 100 116 -458 -933 -1500 -1500
& Roll +395
Units: Focus, X Decenter, Y Decenter: microns
X Tilt, Y Tilt, Roll: arc-seconds
It is interesting to note that in the data shown in Table 5, the maximum travel possible for the X tilt about the mirror vertex is increased with the addition of the optimum roll angle. In the previous tables, only the Y tilt about the vertex was affected by the freedom to vary the roll angle.
Table 6. Maximum Secondary Mirror Motions And Actuator Steps In
The Presence Of A Plus 2.0 Millimeter Focus Motion And
A Minus 2.0 Millimeter X Decenter Motion
Motion Travel Act 1 Act 2 Act 3 Act 4 Act 5 Act 6
Y Dec +1020 -261 -333 -1500 -261 -333 -1500
-2263 326 -1500 -903 326 -1500 -903
X Tilt +3605 -260 -1500 -308 911 -1500 -1499
Vertex -655 -47 -551 -1500 -261 -551 -1282
Y Tilt +4242 -1305 -1500 -899 -496 113 -95
Vertex -633 101 -575 -1378 -19 -816 -1500
Roll +945 102 -879 -1137 -267 -512 -1500
-954 -267 -514 -1500 105 -883 -1134
X Tilt -1628 -280 -605 -1500 -804 -57 -1500
& Roll +1412
Y Tilt +4653 -1500 -1500 -933 -458 116 100
& Roll -395
Y Tilt -951 100 -422 -1500 107 -968 -1500
& Roll -476
Units: Focus, X Decenter, Y Decenter: microns
X Tilt, Y Tilt, Roll: arc-seconds
Table 7. Maximum Secondary Mirror Motions And Actuator Steps In
The Presence Of A Plus 2.0 Millimeter Focus Motion And
A Plus 2.0 Millimeter Y Decenter Motion
Motion Travel Act 1 Act 2 Act 3 Act 4 Act 5 Act 6
X Dec +1441 -1500 16 -605 -1500 16 -605
-1441 -605 16 -1500 -605 16 -1500
X Tilt +6792 -1393 -1500 831 831 -1500 -1393
Vertex -1623 -962 376 -1500 -1500 376 -962
Y Tilt +1537 -1500 -275 -902 -1205 304 -610
Vertex -1537 -610 304 -1205 -902 -275 -1500
Roll +2296 -615 -435 -608 -1500 462 -1493
-2296 -1493 462 -1500 -608 -435 -615
Y Tilt +2294 -1500 -639 -603 -1500 673 -609
& Roll +1146
Y Tilt -2294 -609 673 -1500 -603 -639 -1500
& Roll -1145
Units: Focus, X Decenter, Y Decenter: microns
X Tilt, Y Tilt, Roll: arc-seconds
Table 8. Maximum Secondary Mirror Motions And Actuator Steps In
The Presence Of A Plus 2.0 Millimeter Focus Motion And
A Minus 2.0 Millimeter Y Decenter Motion
Motion Travel Act 1 Act 2 Act 3 Act 4 Act 5 Act 6
X Dec +3820 -1500 -1389 848 -1500 -1389 848
-3820 848 -1389 -1500 848 -1389 -1500
X Tilt +385 -361 -1500 -234 -234 -1500 -361
Vertex -4200 -114 -477 -1500 -1500 -477 -114
Y Tilt +448 -470 -1500 -298 -385 -1328 -213
Vertex -448 -213 -1328 -385 -298 -1500 -470
Roll +447 -254 -1500 -255 -428 -1328 -429
-447 -429 -1328 -428 -255 -1500 -254
Y Tilt +2597 -1500 -1500 -493 -183 -1324 819
& Roll -2115
Y Tilt -2597 819 -1314 -183 -493 -1500 -1500
& Roll +2115
Units: Focus, X Decenter, Y Decenter: microns
X Tilt, Y Tilt, Roll: arc-seconds
Table 9. Maximum Secondary Mirror Motions And Actuator Steps In
The Presence Of A Minus 2.0 Millimeter Focus Motion And
A Plus 2.0 Millimeter X Decenter Motion
Motion Travel Act 1 Act 2 Act 3 Act 4 Act 5 Act 6
Y Dec +2224 -276 1500 943 -276 1500 943
-1021 291 361 1500 291 361 1500
X Tilt +645 73 574 1500 291 574 1285
Vertex -3031 291 1393 486 -740 1393 1500
Y Tilt +617 -69 600 1382 51 839 1500
Vertex -4021 1273 1500 939 495 -59 158
Roll +928 285 540 1500 -65 893 1144
-937 -68 897 1141 285 541 1500
X Tilt +1610 -245 628 1500 824 98 1500
& Roll -1395
X Tilt -3408 338 1453 407 -868 1500 1500
& Roll -123
Y Tilt +919 -70 454 1500 -63 985 1500
& Roll +460
Y Tilt -4489 1500 1500 989 450 -56 -70
& Roll +485
Units: Focus, X Decenter, Y Decenter: microns
X Tilt, Y Tilt, Roll: arc-seconds
Table 10. Maximum Secondary Mirror Motions And Actuator Steps In
The Presence Of A Minus 2.0 Millimeter Focus Motion And
A Minus 2.0 Millimeter X Decenter Motion
Motion Travel Act 1 Act 2 Act 3 Act 4 Act 5 Act 6
Y Dec +2223 943 1500 -276 943 1500 -276
-1021 1500 361 291 1500 361 291
X Tilt +645 1285 574 291 1500 574 73
Vertex -3031 1500 1393 -740 486 1393 291
Y Tilt +4021 158 -59 495 939 1500 1273
Vertex -617 1500 839 51 1382 600 -69
Roll +936 1500 541 285 1141 897 -68
-928 1144 893 -65 1500 540 285
X Tilt +1610 1500 98 825 1500 628 -245
& Roll +1396
X Tilt -3408 1500 1500 -868 407 1453 338
& Roll +124
Y Tilt +4488 -70 -56 450 989 1500 1500
& Roll -485
Y Tilt -919 1500 985 -63 1500 454 -70
& Roll -460
Units: Focus, X Decenter, Y Decenter: microns
X Tilt, Y Tilt, Roll: arc-seconds
Table 11. Maximum Secondary Mirror Motions And Actuator Steps In
The Presence Of A Minus 2.0 Millimeter Focus Motion And
A Plus 2.0 Millimeter Y Decenter Motion
Motion Travel Act 1 Act 2 Act 3 Act 4 Act 5 Act 6
X Dec +3675 -737 1437 1500 -737 1437 1500
-3675 1500 1437 -737 1500 1437 -737
X Tilt +4056 140 513 1500 1500 513 140
Vertex -384 390 1500 260 260 1500 390
Y Tilt +446 237 1329 410 324 1500 497
Vertex -446 497 1500 324 410 1329 237
Roll +447 451 1328 452 282 1500 283
-447 283 1500 282 452 1328 451
Y Tilt +2527 -764 1342 209 531 1500 1500
& Roll -2118
Y Tilt -2527 1500 1500 531 209 1342 -764
& Roll +2118
Units: Focus, X Decenter, Y Decenter: microns
X Tilt, Y Tilt, Roll: arc-seconds
Table 12. Maximum Secondary Mirror Motions And Actuator Steps In
The Presence Of A Minus 2.0 Millimeter Focus Motion And
A Minus 2.0 Millimeter Y Decenter Motion
Motion Travel Act 1 Act 2 Act 3 Act 4 Act 5 Act 6
X Dec +1429 638 18 1500 638 18 1500
-1429 1500 18 638 1500 18 638
X Tilt +1543 986 -327 1500 1500 -327 986
Vertex -6672 1466 1500 -785 -785 1500 1466
Y Tilt +1504 634 -278 1211 925 311 1500
Vertex -1504 1500 311 925 13211 -278 634
Roll +2249 1500 -408 1493 641 438 635
-2249 635 438 641 1493 -408 1500
Y Tilt +2259 634 -637 1500 641 674 1500
& Roll -1134
Y Tilt -2259 1500 674 641 1500 -637 634
& Roll -1134
Units: Focus, X Decenter, Y Decenter: microns
X Tilt, Y Tilt, Roll: arc-seconds
VI. Summary Of Maximum Travel For Each Mirror Motion
In an effort to provide a more concise presentation of the data from Tables 5 through 12, a summary of the maximum achieved motions for each motion combination is presented in Table 13. In this table two values are given for each mirror motion for each condition. A given condition is where a particular set of one or two mirror motions have been applied to the mirror. The upper value is the maximum motion achieved in the positive motion direction and the lower value is the maximum motion achieved in the negative motion direction. For those situations where further travel of a given mirror motion was possible if the mirror roll motion was optimized, an additional pair of rows of data are included in the table showing only those motions for which the maximum travel was increased.
Table 13. Summary of Maximum Secondary Mirror Motions
Maximum Mirror Motion
Applied Focus X Dec Y Dec X Tilt Y Tilt Roll
Motions microns microns microns arc-sec arc-sec arc-sec
none +4285 4823 4203 5363 5189 7778
-4198 -4823 -4290 -5446 -5189 -7778
roll opt. 6173
-6173
focus +2mm N/A 2600 4645 3574 2762 4123
N/A -2600 -2243 -2893 -2762 -4123
focus +2mm 3346
roll opt. -3346
focus -2mm N/A 2581 2243 2817 2725 4141
N/A -2581 -4351 -3543 -2725 -4141
focus -2mm 3248
roll opt. -3248
focus +2mm N/A N/A 1022 3605 633 954
X Dec +2mm N/A N/A -2263 -655 -4242 -945
focus +2mm 3605 951
X Dec +2mm -1628 -4653
roll opt.
focus +2mm N/A N/A 1020 3605 4242 945
X Dec -2mm N/A N/A -2263 -655 -633 -954
focus +2mm 3605 4653
X Dec -2mm -1628 -951
roll opt.
focus +2mm N/A 1441 N/A 6792 1537 2296
Y Dec +2mm N/A -1441 N/A -1623 -1537 -2296
focus +2mm 2294
Y Dec +2mm -2294
roll opt.
focus +2mm N/A 3820 N/A 385 448 447
Y Dec -2mm N/A -3820 N/A -4200 -448 -447
focus +2mm 2597
Y Dec -2mm -2597
roll opt.
focus -2mm N/A N/A 2224 645 617 928
X Dec +2mm N/A N/A -1021 -3031 -4021 -937
focus -2mm 1610 919
X Dec +2mm -3408 -4489
roll opt.
focus -2mm N/A N/A 2223 645 4021 936
X Dec -2mm N/A N/A -1021 -3031 -617 -928
focus -2mm 1610 4488
X Dec -2mm -3408 -919
roll opt.
focus -2mm N/A 3675 N/A 4056 446 447
Y Dec +2mm N/A -3675 N/A -384 -446 -447
focus -2mm 2527
Y Dec +2mm -2527
roll opt.
focus -2mm N/A 1429 N/A 1543 1504 2249
Y Dec -2mm N/A -1429 N/A -6672 -1504 -2249
focus -2mm 2259
Y Dec -2mm -2259
roll opt.