The different kinds of inhomogeneities that may occur in glasses are discussed. Inhomogeneity of glasses depends upon: (a) the melting process; (b) the density variations due to thermodynamic imbalance; (c) the permanent strains resulting from temperature gradients in the annealing range. If the highest possible optical homogeneity of glass must be achieved, it is necessary to know the influence of (a), (b), and (c). By eliminating the inhomogeneities resulting from (b) and (c), the inhomogeneity resulting from the melting process can be measured. To achieve reliable test data on the inhomogeneity of a specific glass, two different measuring methods should be used. The best homogeneity that means the smallest variation of refractive index Δn = ±3 × 10−7 was achieved with a BK7 disk having a diameter of 400 mm and a thickness of 47 mm. Further examples are also discussed.
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Inhomogeneities, Resulting from Melting and Annealing Process, of BK 7 Disk (Diameter 400 mm, Thickness 47 mm)a
Sample
Measurement of homogeneity (K0 minus Kx) after precision annealing Homogeneity resulting from melting process (a) plus annealing (b)
Measurement of homogeneity (K0 minus Kx) after thermal treatment in laboratory (super precision annealing) Homogeneity resulting from melting process (a) only
Measured according to the statistical method, Fig. 2.
Mean error of individual measurement
.
Table II
Inhomogeneities, Resulting from Melting and Annealing Process of a Plate, 1.500 mm × 1.500 mm × 200 mm Glass Type BK 7 (Measured According to the Statistical Method, Fig. 2)
Sample
Measurement of homogeneity (K0 minus Kx) after precision annealing Homogeneity resulting from melting process (a) plus annealing (b)
Measurement of homogeneity (K0 minus Kx) after thermal treatment in laboratory (super precision annealing) Homogeneity resulting from Melting process (a) only
(a + b) minus (a)
K0
0
0
K1
+5 × 10−7
±0 × 10−7
+5 × 10−7
K2
+23 × 10−7
+5 × 10−7
+18 × 10−7
K3
+16 × 10−7
+9 × 10−7
+7 × 10−7
K4
+5 × 10−7
+3 × 10−7
+2 × 10−7
K5
+3 × 10−7
+5 × 10−7
−2 × 10−7
K6
+17 × 10−7
+11 × 10−7
+6 × 10−7
K7
+7 × 10−7
+2 × 10−7
+5 × 10−7
K8
+18 × 10−7
+7 × 10−7
+11 × 10−7
K9
+16 × 10−7
+5 × 10−7
+11 × 10−7
K10
+24 × 10−7
+3 × 10−7
+21 × 10−7
K11
−8 × 10−7
−12 × 10−7
−5 × 10−7
K12
−23 × 10−7
−12 × 10−7
−11 × 10−7
K13
−3 × 10−7
−6 × 10−7
+3 × 10−7
Δnmax
+24 × 10−7 to −23 × 10−7
+11 × 10−7 to −12 × 10−7
Table III
Inhomogeneities, Resulting from Melting and Annealing Process of a Plate (1.500 mm × 1.500 mm × 200 mm) Glass Type BK 7 (Measured According to the Statistical Method, Fig. 2)
Sample
Measurement of homogeneity (K0 minus Kx) after precision annealing Homogeneity resulting from melting process (a) plus annealing (b)
Measurement of homogeneity (K0 minus Kx) after thermal treatment in laboratory (super precision annealing) Homogeneity resulting from melting process (a) only
(a + b) minus (a)
K0
0
0
K1
−6 × 10−7
−1 × 10−7
−5 × 10−7
K2
+12 × 10−7
+5 × 10−7
+7 × 10−7
K3
+20 × 10−7
+9 × 10−7
+11 × 10−7
K4
−23 × 10−7
−12 × 10−7
+11 × 10−7
K5
+6 × 10−7
+3 × 10−7
+3 × 10−7
K6
+13 × 10−7
+4 × 10−7
+9 × 10−7
K7
−15 × 10−7
−7 × 10−7
−8 × 10−7
Δnmax
+20 × 10−7 to −23 × 10−7
+9 × 10−7 to −12 × 10−7
Table IV
Inhomogeneities, Resulting from Melting and Annealing Process, Glass Type BK 7 (Size 400 mm × 400 mm × 100 mm) (Measured According to the Statistical Method, Fig. 2)
Sample
Measurement of homogeneity (K0 minus Kx) after precision annealing Homogeneity resulting from melting process (a) plus annealing (b)
Measurement of homogeneity (K0 minus Kx) after thermal treatment in laboratory (super precision annealing) Homogeneity resulting from melting process (a) only
(a + b) minus (a)
K0
0
0
K1
−15 × 10−7
−4 × 10−7
−11 × 10−7
K2
−18 × 10−7
−8 × 10−7
−10 × 10−7
K3
+13 × 10−7
+6 × 10−7
+7 × 10−7
K4
+4 × 10−7
+3 × 10−7
+1 × 10−7
K5
−6 × 10−7
+1 × 10−7
−7 × 10−7
K6
+15 × 10−7
+10 × 10−7
+5 × 10−7
K7
+10 × 10−7
+8 × 10−7
+2 × 10−7
K8
+8 × 10−7
+1 × 10−7
+7 × 10−7
K9
+8 × 10−7
+5 × 10−7
+3 × 10−7
K10
+18 × 10−7
+8 × 10−7
+10 × 10−7
Δnmax
+18 × 10−7 to −18 × 10−7
+10 × 10−7 to −8 × 10−7
Tables (4)
Table I
Inhomogeneities, Resulting from Melting and Annealing Process, of BK 7 Disk (Diameter 400 mm, Thickness 47 mm)a
Sample
Measurement of homogeneity (K0 minus Kx) after precision annealing Homogeneity resulting from melting process (a) plus annealing (b)
Measurement of homogeneity (K0 minus Kx) after thermal treatment in laboratory (super precision annealing) Homogeneity resulting from melting process (a) only
Measured according to the statistical method, Fig. 2.
Mean error of individual measurement
.
Table II
Inhomogeneities, Resulting from Melting and Annealing Process of a Plate, 1.500 mm × 1.500 mm × 200 mm Glass Type BK 7 (Measured According to the Statistical Method, Fig. 2)
Sample
Measurement of homogeneity (K0 minus Kx) after precision annealing Homogeneity resulting from melting process (a) plus annealing (b)
Measurement of homogeneity (K0 minus Kx) after thermal treatment in laboratory (super precision annealing) Homogeneity resulting from Melting process (a) only
(a + b) minus (a)
K0
0
0
K1
+5 × 10−7
±0 × 10−7
+5 × 10−7
K2
+23 × 10−7
+5 × 10−7
+18 × 10−7
K3
+16 × 10−7
+9 × 10−7
+7 × 10−7
K4
+5 × 10−7
+3 × 10−7
+2 × 10−7
K5
+3 × 10−7
+5 × 10−7
−2 × 10−7
K6
+17 × 10−7
+11 × 10−7
+6 × 10−7
K7
+7 × 10−7
+2 × 10−7
+5 × 10−7
K8
+18 × 10−7
+7 × 10−7
+11 × 10−7
K9
+16 × 10−7
+5 × 10−7
+11 × 10−7
K10
+24 × 10−7
+3 × 10−7
+21 × 10−7
K11
−8 × 10−7
−12 × 10−7
−5 × 10−7
K12
−23 × 10−7
−12 × 10−7
−11 × 10−7
K13
−3 × 10−7
−6 × 10−7
+3 × 10−7
Δnmax
+24 × 10−7 to −23 × 10−7
+11 × 10−7 to −12 × 10−7
Table III
Inhomogeneities, Resulting from Melting and Annealing Process of a Plate (1.500 mm × 1.500 mm × 200 mm) Glass Type BK 7 (Measured According to the Statistical Method, Fig. 2)
Sample
Measurement of homogeneity (K0 minus Kx) after precision annealing Homogeneity resulting from melting process (a) plus annealing (b)
Measurement of homogeneity (K0 minus Kx) after thermal treatment in laboratory (super precision annealing) Homogeneity resulting from melting process (a) only
(a + b) minus (a)
K0
0
0
K1
−6 × 10−7
−1 × 10−7
−5 × 10−7
K2
+12 × 10−7
+5 × 10−7
+7 × 10−7
K3
+20 × 10−7
+9 × 10−7
+11 × 10−7
K4
−23 × 10−7
−12 × 10−7
+11 × 10−7
K5
+6 × 10−7
+3 × 10−7
+3 × 10−7
K6
+13 × 10−7
+4 × 10−7
+9 × 10−7
K7
−15 × 10−7
−7 × 10−7
−8 × 10−7
Δnmax
+20 × 10−7 to −23 × 10−7
+9 × 10−7 to −12 × 10−7
Table IV
Inhomogeneities, Resulting from Melting and Annealing Process, Glass Type BK 7 (Size 400 mm × 400 mm × 100 mm) (Measured According to the Statistical Method, Fig. 2)
Sample
Measurement of homogeneity (K0 minus Kx) after precision annealing Homogeneity resulting from melting process (a) plus annealing (b)
Measurement of homogeneity (K0 minus Kx) after thermal treatment in laboratory (super precision annealing) Homogeneity resulting from melting process (a) only