Optical Design & Aberrations

Periscope Optics Specifications

A periscope with the following optical  specifications is described below:

Magnification                      1½            6x           12x

Field of View                       32°            8°            4°

Aperture (mm)                     10.5          42            42

Exit Pupil (mm)                      7              7              3.5

Periscope length is 45 ft.;   outer tube diameter, 7.5 in.;  maximum  lens diameters, 4 in..

Elevation range of the line of sight is -15° to +80°.

Image relative illumination at the edge of field is 40%.

The description of the optics begins at the top of the periscope with the head window and proceeds downwards to the last component in the optical train, the eyepiece. The commentary is from the optical designer’s perspective.

Head Optics:   Window and Right Angle Prism

Sub periscopes allow viewing of the entire surrounding hemisphere. In the horizontal direction, the periscope line of sight (LOS) is swept 360° by  rotation of the entire  periscope in its bearings. In the vertical direction,  the LOS is slued from   -15° to +80° or more by operator rotation of the periscope training handle. This action causes the periscope head prism to rotate about a horizontal axis, positioning  the LOS at a chosen elevation angle.Periscope Head Ray Trace copy

The illustration to the right shows the ray bundle paths through the prism and the window over the design elevation range.

High elevation angles result in a long head window. The width of the window is determined by the ray bundle intercepts on the window  at high and low magnifications.

Tilt angle of the window impacts window length. A steeper angle results in a shorter window  but reduces the available area above the window for other sensors such as antennas.

The window  must withstand the high pressure of deep ocean submergence without fracture or leakage.  This largely  determines the window material properties and design. Also,  the window  material’s thermal characteristics must be suitable for window de-icing.

Window heating is provided either by an electrically conductive coating on the interior surface of the window or by fine electrical wires embedded in a sandwich style window. The EC coating degrades light transmission to a degree. The wireheated head window improves light transmisssion and improves de-icing by locating the heat source nearer to the external window surface..

The window must  withstand frequent cleaning in the field while maintaining surface polish and flatness. Fused silica is one window material  which provides the required mechanical properties while meeting the optical specifications..

High optical performance of the head window is critical to high performance of the entire periscope. An optical wavefront distorted by the head window precludes high image quality, even in a perfect periscope.

The head prism is an ordinary right angle prism manufactured from precision optical glass. Glass light absorption must be low due to the long optical path through the prism. Spectral transmission uniformity must be  high to avoid a yellowish image caused by lower blue light transmission. The prism  entrance face,  exit face and hypotenuse are ground and polished flat to a high degree, exactly as for the head window. The entrance and exit faces are anti-reflection coated and the hypotenuse is silvered and protective coated..

Objective Lens and Telemeter Assembly

The objective lens assembly is made up of a cemented doublet achromat, air-spaced doublet field lens, telemeter-collector lens and telemeter window. Ths unit is housed in the tapered neck section of the periscope. Periscope Objective Lens Ass'y copy

The obective lens and objective field lens form an image of the object or scene. The image  is coincident with the telemeter etched plane inner surface. It is largely corrected of aberrations so the telemeter pattern and scene image appear to be exactly superimposed on one another.

The telemeter pattern, shown below, is graduated to allow object range determination when the object  dimensions are known.

Periscope Reticle TOD copyThe reticle pattern is  illuminated  with red light for night time viewing.

A plano-convex  collector lens is cemented to the telemeter. This serves two functions. First, off-axis image rays are redirected to be kept within the diameter of the  inner tube in which the relay lenss are mounted.  Secondly, the  substantial thickness of the lens prevents dust or other air-borne particles from coming into contact with the reticle surface. Dust and other foreign particles on the convex exterior surface of the lens will be substantially out of focus.

The last component in the unit, the telemeter sealing window, serves a similar role. Dust on its surface will not be viewable since it is  very far out of focus. This is also the case with the relay lenses and collector lenses which follow below..

Galilean Telescope: 1½x Magnification

Periscope magnification is changed from 6x to 1½x by introducing a ¼x Galilean telescope into the optical path in front of the 6x objective lens.

Sub Periscope Gaslilean + Head Window & prism_Rev A copyField of view is increased from 8° in 6x  to 32° in 1½x.

The reversed 4x Galilean telescope consists of a negative power eyelens, the top lens in the illustration at the left, and a positive power objective lens located near the 6x objective lens.

These lenses are individuallly mounted in cube-like structures  (not shown) which rotate the lenses in and out  of the optical path. By this technique additional storage space is not required  for the lenses when they are not in use.

A key feature of the reversed Galilean is the nearness of its entrance pupil to the head prism. This keeps the size of the head prism at a minimum as can be observed in the ray diagram at the left. Sufficient clearance must be provided, however, to allow the head prism to be rotated without interference while slewing the line of sight in elevation.

The prism is dimensioned to be large enough to permit passage of the 32° field over most of the elevation range, -15° to +80°. Field of view vignetting  is ultimately  incurred at the higher elevation angles.

Periscope Relay Optics

The image formed by the objective lens system is relayed down the tube to the eyepiece  by a relay lens system. In this case the relay system is made up of  three relay lens pairs like the one shown at the right. It is the central relay lens set. The total distance covered by the three relay lens sets is about 10 meters, or about 4 meters per set..Relay Lens System copy

A pair of long focal length lenses, R3 and R4  in the  ray diagram at the right, are focused on the input and output images.  Their separation is the maximum consistent with the image relative illumination requirement, as discussed below.

The collimated light space between the relay lenses can be increased to gain track length without changing focus. However, as the space between the lenses increases there is progressive loss of light for off-axis image points.  This is illustrated in the diagram below of the ray bundle pupils at the aperture stop.

Periscope Pupils copyThe “cat’s eye” pupil defines the image relative illumination, that is the illumination at the edge of the field of view compared to the center. The edge pupil is defined by the apertures of the two relay lenses, R3 and R4. It is approximately 40%. The fall-off in light is rarely perceived by the operator, however. This is because the viewer’s eye pupil diameter, when viewing  daylight outdoor scenes, is typically only two or three millimeters compared to the   7 mm exit pupil of the periscope.

Relay Lens Achromat (Rev C)The relay lens is an achromat made up of ordinary crown and flint optical glasses. It is air spaced and not  cemented as is common for doublet achromats. This gives the optical designer greater control over the correction of spherical aberration. This aberration must be reduced to a very small  amouint, of the order of λ/30  or bettter, if a total of λ/4 is the total allowed in the periscope  which consists of six relay lenses and an objective lens.

In addition, the doublet is not cemented to prevent stress in the glass, and possible breakage, when the lenses are subjected to temperature extremes, such as  at sea or dockside.

The last relay lens set, R5-R6,  which is identical to the R3-R4 set,  delivers the image to the eyepiece box at the lower end of the mast.

2x Galilean Telescope: 12x Magnification

12x periscope magnification is achieved by switching a 2x Galilean telescope into the collimated light region between relay lenses, R3 and R4. The lenses are mounted and switched in and out in a manner similar to the ¼x Galilean in the head. The space between the objective and eyelens is made as long as possible in order to keep lenses as optically weak as possible so as to not adversely affect field curvature aberration correction.

Eyepiece Box Optics and Eyepiece

Eyepiece, Prism & Staunching Window_edited-1The final relayed  image  is delivered to the  Eyepiece  Box  which is attached to the  lower end of the mast. The eyepiece is mounted on a removable plate that attaches to the Eyepiece Box.

The Eyepiece Box contains a right angle prism and the staunching window

The tightly sealed staunching window maintains  the mast’s pressurized dry nitrogen atmosphere  sea water out of the sub  in the event of a flooded  periscope.

The image delivered to the eyepiece box is formed within  a  right angle prism as shown in the ray diagram above. The image is located  sufficiently far from the prism entrance surface to prevent dust or other foreign matter on its surface from being viewed with the image.

The eyepiece provides an apparent field of nominally 48° in the three modes, 1½x, 6x, and 12x. The exit pupil is 7mm, the maximum opening of the human eye pupil under low light levels. A large eye relief is provided for operators with eyeglasses. Diopter adjustment is also  provided. Additional viewer aids include heating to eliminate condensation, “binocular”  blinder for the non-viewing eye,  and a brow rest for maintaining eye position.

Image Quality

Periscope image quality is very high, the image being substantially free of spherical aberration. This is remarkable given the many lenses in the optical train.. The plot below shows the wavefront optical path difference (OPD) across the system pupil for the on-axis image, at the 587.6 nm wavelength  (yellow).

Periscope Wavefront OPD

Correction of spherical aberration is better than λ/10, resulting in an image which is virtually undegraded in monochromatic light,

Aberrations in white light are a much different story. The periscope employs achromats throughout but there remains  a very large residual color aberration, the “secondary spectrum”. This is illustrated in the plot below which shows the aberrations for the on-axis  white light image.

Seconndary Spectrum Rev A copy

The secondary spectrum aberration is enormous, 5 wavelengths of optical path difference between the central  yellow-green wavelengths and the color-corrected  blue and red wavelengths.

The secondary spectrum can also be  expressed in terms of the  transverse ray aberrations at the eyepiece image plane. These are shown in the plot to the left. Periscope HTan U (Rev B) copyThe total blur size approaches 0.25 mm, grossly larger than the 0.010 mm diffraction spot size for an aberration-free system..

It would be reasonable to assume that the observed white light imagery would be quite poor. This is not necessarily the case, however, as  is discussed below.

There are two factors which allow the periscope to yield excellent image quality despite the large secondary spectrum aberration.Eye Response copy


First, the pupil diameter of the human eye under bright scene conditions is only 2-3 mm, not the full 7 mm exit pupil diameter of the periscope. Therefore, the eye pupil effectively acts as the system aperture stop and reduces the aberrations proportionately.

Secondly, the spectral response of the human eye, shown above to the right,  weights the viewed spectrum colors differently, with emphasis being on the central geen and green-yellow wavelengths. Thus, the negative impact of the out-of-focus red and blue ends of the spectral band are greatly mitigated.

These effects can be expressed quantitatively through the modulation transfer function (MTF) of the system. The MTF for the optics with full 7.0 mm exit pupil and equal weighting assigned to all wavelengths is shown along side the MTF of the system with 2.5 mm aperture and eye response wavelength weightings.

Periscope MTF (merged layers) copy

Ther MTF for the case of the 2.5 mm pupil approaches the MTF for a perfect diffraction limited optical system of the same aperture. This confirms the actual viewing experience that the periscope image appears crisp and bright like a high quality binocular or telescope.















3 thoughts on “Optical Design & Aberrations

  1. Hello,

    I am looking to connect with a SME in the field of optical periscopes. I am currently working on a building project and we would like to incorporate a 30′ periscope on top of our facility that would allow youth from the City Heights community in San Diego, see the ocean apprx. 13 miles away. Any direction, advice or information would be greatly appreciated.

    Thank you,

    • Field curvature (longitudinal)of the relay lenses, typically six in number, plus that of the objective lens can be as large as a few millimeters. However, the tangential field can be made flat by properly configuring the lenses and the space between them, leaving astigmatism as the limiting aberration. Vignetting up to 40% at the edge of the field has proven acceptable in many applications and is a very useful variable in the design work.

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