4-Point Mirror Cells

4-Point Cells

4-point cells provide improved support over 3-point cells for some 10-inch and 12-inch mirrors. I have included them also because they may be useful for mirrors equipped with warping harneses such as those used by Arthur Leonard in his Yolo off-axis telescopes. The 4-point cells described here all use four support points arranged equidistant around a circle. Two of the points are located on a pivoted bar. The bar pivot point is midway between the two mirror support points.

The other possibility for a symmetric 4-point arrangement has three points equidistant around a circle and one point at the center. This latter design has been investigated by others, and found not to perform well.

Diagram of four 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.)
r₁ = Radius of circle on which bar pivot point lies as a fraction of mirror blank radius.
d = Distance separating the two support points on the bar as a fraction of mirror blank radius.
r₂ = 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
Diameter	Thickness	f/	Obs. Dia.	r₁	d	r₂	P-V	RMS	Focus Shift
4.25	0.625	12	0	0.357	0.714	0.505	1/405	1/2180
4.25	1	12	0	0.347	0.694	0.491	1/506	1/3360
6	0.8	12	0	0.359	0.718	0.508	1/184	1/966
6	1.2	12	0	0.350	0.700	0.495	1/157	1/851
8	1.1	12	0	0.359	0.717	0.507	1/107	1/566
8	1.35	12	0	0.354	0.708	0.500	1/127	1/718
10	1.3	12	0	0.360	0.720	0.509	1/64	1/336
10	1.3	8	1.52	0.364	0.724	0.512	1/62	1/324
10	1.3	6	1.83	0.364	0.727	0.514	1/60	1/315
10	1.85	12	0	0.352	0.703	0.497	1/85	1/503
12	1	5.3	2.36	0.377	0.753	0.533	1/22	1/101	-0.062mm
12	2.00	5	2.14	0.358	0.717	0.507	9.36nm 1/53	1.68nm 1/298	-0.015mm
12.5	1.5	12	0	0.362	0.724	0.512	1/38	1/192
12.5	1.5	8	1.83	0.364	0.727	0.514	1/36	1/185
12.5	1.5	6	1.83	0.366	0.732	0.517	1/35	1/180
12.5	2.00	5	2.14	0.3593	0.7186	0.5081	10.6 nm 1/47	1.91 nm 1/262	-0.018 mm
12.5	2.2	12	0	0.353	0.706	0.499	1/53	1/307
12.5	2.2	8	1.83	0.355	0.709	0.501	1/53	1/300
12.5	2.2	6	1.83	0.356	0.711	0.503	1/53	1/295

Plate Glass
Diameter	Thickness	f/	Obs. Dia	r₁	d	r₂	P-V	RMS	Focus Shift
4.25	0.7	12	0	0.354	0.709	0.501	1/376	1/2107
4.25	1	12	0	0.347	0.694	0.491	1/506	1/3360
6	0.8	12	0	0.359	0.718	0.508	1/156	1/822
6	1	12	0	0.354	0.707	0.500	1/190	1/1070
200mm	15mm	7	40mm	0.375	0.751	0.531	1/44	1/202	-0.055mm
8	0.75	6	1.52	0.372	0.743	0.526	1/52	1/247	-0.032mm
8	0.875	12	0	0.363	0.727	0.514	1/70	1/349
8	1.1	12	0	0.358	0.716	0.507	1/91	1/481
8	1.375	12	0	0.353	0.706	0.499	1/108	1/621
10	0.875	12	0	0.368	0.736	0.520	1/33	1/155
10	0.875	8	1.52	0.371	0.741	0.524	1/32	1/147
10	0.875	6	1.83	0.373	0.747	0.528	1/30	1/140
10	1.3	12	0	0.360	0.708	0.508	1/55	1/286
10	1.3	8	1.52	0.361	0.723	0.511	1/53	1/276
10	1.3	6	1.83	0.363	0.726	0.514	1/51	1/268
10	1.75	12	0	0.353	0.706	0.499	1/83	1/477
12.5	1.5	12	0	0.362	0.724	0.512	1/38	1/192
12.5	1.5	8	1.83	0.363	0.727	0.514	1/31	1/158
12.5	1.5	6	1.83	0.366	0.732	0.517	1/35	1/180
12.5	1.5	5	2.14	0.367	0.734	0.519	1/29	1/150
12.5	2.125	12	0	0.353	0.706	0.500	1/44	1/252
12.5	2.125	8	1.83	0.355	0.711	0.502	1/52	1/289
12.5	2.125	6	1.83	0.356	0.712	0.504	1/43	1/242
12.5	2.125	5	2.14	0.357	0.714	0.505	1/43	1/238