ABSTRACT
Sometimes it is desirable to prevent an image from moving due to the vibration of the optical system. This occurs, for example, in TV coverage of events from a helicopter, telescope (or a binocular at high magnifications) viewing from the deck of a boat, or action scenes where the cinematographer is moving. This stabilization of the image may be accomplished in several ways:
A liquid-filled wedge plate may be placed in front of the lens. One of the plates is tilted to keep the image fixed in relation to the case as the complete system is moved (De La Cierva 1965). A thin wedge prism will deviate the beam by an angle θ = ϕ(N − 1), where N is the refractive index of the fluid, θ is the deviation angle, and ϕ is the wedge angle between the two plates. The liquid-filled wedge has the advantage of being able to be placed in front of a wide variety of optical systems. It generally has a higher bandwidth of frequency response than the other systems.
A group of lenses may be tilted or displaced to maintain the fixed image location (Furukawa 1976; Hayakawa 1998; Suzuki 1999).
An internal mirror (gyro stabilized) may be tilted to maintain the fixed image location (Kawasaki et al. 1976; Helm and Flogaus 1981).
An inertial prism (gyro stabilized) may be used to maintain the fixed image location (Humphrey 1969). This system is shown schematically in Figure 40.1. M 1 is the objective-relay assembly of focal length 10.0, whereas the gyro-stabilized prism is shown as M 2. The system is shown in Figure 40.2 with the prism assembly in line with the objective. A concave mirror at the focus of the front objective is used as a field lens; however, the actual system tilts the beam with the concave mirror. A final objective images the collimated beam onto the image surface. The front objective is the same as shown in Figure 2.3 whereas the other two objectives are simply are a 0.5 scale of this. The complete system has an effective focal length of 10.0 and so if not stabilized, a 2° tilt would correspond to an image displacement of 0.349, whereas with stabilization the displacement is only 0.000178 (chief ray values). Case stabilization. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/fig40_1.tif"/> Stabilized lens system. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/fig40_2.tif"/>
Referring to Figure 40.1, M 1 = θ 2 θ 1 . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq180.tif"/>
For stabilization, the exiting ray must make an angle with the optical 444axis that is the same as before the tilt: θ 1 − M 2 ( θ 2 − θ 1 ) = 0.0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq181.tif"/> θ 1 − M 2 ( θ 1 M 1 − θ 1 ) = 0.0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq182.tif"/> M 2 ( M 1 − 1.0 ) = 1.0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315222295/bd2ad0d9-a48e-40ac-8986-c51474069cbd/content/eq183.tif"/>
Because M 2 has an odd number of reflections, M 2 = 1.0 (as per the above sign convention) and M 1 = 2.0.
The following system is shown for an axial beam only (Table 40.1). Case-Stabilized System
Surface
Radius
Thickness
Material
Diameter
0
0.0000
0.1000E+11
0.000
1
0.0000
0.0000
0.000
2
6.4971
0.3500
N-BAK1
2.000 Stop
3
−4.9645
0.2000
SF1
2.020
4
−17.2546
9.7267
2.002
5
−6.6660
−4.8663
Mirror
0.040
6
−8.6273
−0.1000
SF1
1.022
7
−2.4823
−0.1750
N-BAK1
1.031
8
3.2486
−0.5000
1.041
9
0.0000
0.0000
0.000
10
0.0000
−0.5000
N-BK7
1.040
11
0.0000
0.0000
0.000
12
0.0000
0.5517
Mirror
1.144
13
0.0000
0.0000
0.000
14
0.0000
−0.7779
Mirror
1.596
15
0.0000
0.0000
0.000
16
0.0000
0.5517
Mirror
1.144
17
0.0000
0.0000
0.000
18
0.0000
0.5000
1.046
19
0.0000
0.0000
0.000
20
3.2486
0.1750
N-BAK1
1.046
21
−2.4823
0.1000
SF1
1.036
22
−8.6273
4.8610
1.027
23
0.0000
0.0000
0.001
The significance of some of these surfaces is noted below:
Surfaces 1, 9, and 19 are used to test the system for stabilization (rotate M 1).
445Surfaces 2–4 have a front objective of focal length 10.0.
Surface 5 is the concave mirror functioning as a field lens.
Surfaces 6–8 comprise a collimating lens of 5.0 focal length.
Surfaces 10–18 is the stabilized prism, M 2.
Surfaces 20–22 comprise the final imaging lens of 5.0 focal length.
Surface 23 is the final image that is then viewed with an eyepiece.
Hydrostatic compensation may be used (Humphrey 1970). In this method, the line of sight is reflected off of a plane mirror in a fluid-filled chamber that will not follow motions of the housing. The output beam then remains stable for accidental motion of the housing.
