3-Point Cells

Diagram of three point cell

Diameter = Mirror Blank Diameter in Inches
Thickness = Mirror Blank Edge Thickness in Inches
f/ = Focal Length in Inches / Diameter
Obs Dia. = Central Obstruction Diameter in Inches (This is usually the diagonal mirror minor axis.)
r = Radius of circle on which support points lie as a fraction of mirror blank radius
P-V = Peak to Valley Mirror Deformation with this cell in Waves (1 wave = 500nm)
RMS = Root Mean Square Mirror Deformation with this cell in Waves (1 wave = 500nm)

Pyrex
DiameterThicknessf/Obs. Dia.rP-VRMS
311200.3921/8401/5000
3180.750.3691/9291/5000
3160.750.3381/10681/6000
4.250.6251200.4061/2361/1120
4.250.62581.00.3811/2461/1111
4.250.62561.00.3831/2391/1083
4.2511200.3981/3481/2000
4.25181.00.3771/3751/1990
4.25161.00.3781/3701/1967
60.81200.4071/1071/486
60.881.30.3871/1081/476
60.861.30.3901/1051/462
61.21200.4011/1571/851
61.281.30.3841/1641/837
61.261.30.3851/1611/824
81.11200.4061/621/256
81.181.30.3991/621/279
81.161.520.3961/611/272
81.351200.4041/761/385
81.3581.30.3971/771/378
81.3561.520.3931/761/371
101.31200.4071/371/167
101.381.520.4011/371/163
101.361.830.3981/361/158
101.851200.4021/531/228
101.8581.520.3971/531/269
101.8561.830.3941/531/268
12.51.51200.4081/211/94
12.51.581.830.4031/201/91
12.51.561.830.4061/201/88
12.51.552.140.4051/191/86
12.52.21200.4031/321/167
12.52.281.830.3991/321/164
12.52.261.830.4001/321/161
12.52.252.140.3981/321/158

Plate Glass
DiameterThicknessf/Obs. DiarP-VRMS
4.250.71200.4041/2651/1320
4.250.781.00.3801/2781.1309
4.250.761.00.3821/2751/1281
4.2511200.3981/3491/2006
4.25181.00.3771/3751/1990
4.25161.00.3781/3701/1967
60.37561.30.4061/231/105
60.561.30.3981/431/193
60.7561.30.3901/811/354
60.81200.4071/1071/484
60.881.30.3871/1091/475
60.861.30.3901/1051/462
611200.4041/1341/673
6181.30.3851/1391/664
6161.30.3871/1361/650
80.7561.520.4051/251/113
80.8751200.4091/431/195
80.87581.30.4011/421/189
80.87561.520.3991/411/183
81.11200.4061/621/286
81.181.30.3991/621/279
81.161.520.3961/611/272
81.3751200.4041/771/395
81.37581.30.3961/781/387
81.37561.520.3931/771/380
100.8751200.4111/181/83
100.87581.520.4061/171/80
100.87561.830.4051/171/76
101.31200.4071/371/167
101.381.520.4011/371/163
101.361.830.3981/361/158
101.751200.4031/501/259
101.7581.520.3981/511/254
101.7561.830.3941/501/249
12.51.51200.4071/181/80
12.51.581.830.4031/201/91
12.51.561.830.4061/201/88
12.51.552.140.4051/191/86
12.52.1251200.4031/271/135
12.52.12581.830.3981/271/133
12.52.12561.830.4001/261/130
12.52.12552.140.3981/261/128

BVC
DiameterThicknessf/Obs. DiarP-VRMS
8161.520.3981/511/226
101.2561.830.3991/331/148
121.561.830.4071/221/100
12.51.561.830.4091/191/86


The following table shows a slightly different approach to arranging the 3-point cell data. This table gives support radii optimised for a range of mirror diameters and thicknesses. These were calculated for plate glass mirrors, but the differences for Pyrex or BVC are small enough to be ignored. All of these designs result in no more than 2.5 nm RMS deformation of the mirror surface (1/200 wave). This allows some room for construction tolerances with a reasonable probability that the finished cell - mirror combination will perform well, even for high resolution work. The designs assume that focal ratio is 5 and a reasonably sized diagonal is present. Moderate changes in focal ratio will not have large effects, except perhaps on very thin mirrors.

Plop Optimized Radii for 3-Point Cells
 Thickness (mm)
Diameter (mm)
100
150
200
250
317.5
 6  10  15  20  25  33.3  37  42  53
 20.2  19.3  19  18.8  18.65        
     29.1  28.72  28.5        
         38.9  38.5      
             47.88  47.75  
                 61.60

 
 

2002 Mark D. Holm
Revised January 21, 2005

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