Window & Prism Ray Trace

Periscope Head Design

Submarine periscope head and neck are typically small and slender to reduce detectability either  by direct view or by mast wake. Therefore, small, compact optics are necessary, but the optics must also meet the fundamental  system requirements of  aperture, field of view and elevation scan range.  .

Prism and window design are performed in concert with the  periscope mechanical design. Considerations include window and seal integrity at deep submergence,  space claims for other periscope sensors and associated electronics, electrical  signal and power transmission  lines. Mast vibration and flexure  as well as small visual and radar cross-sections are equally important considerations. Iterative design work between the optical, mechanical, electrical, microwave and system engineers involving performance  trade-offs is typically required..

Periscope head window and prism ray tracing

Periscope head window and prism ray tracing  is used to determine their size, location and orientation. Therefore, a ray trace model needs to address the minimum and maximum line of sight scan angles, entrance pupil diameters,  fields of view,  window inclination angle, prism pivot point location, prism refractive index and, very importantly, the entrance pupil location of the periscope optics which follow..Periscope Head Window, Prism Ray Trace 90 Deg

The ray trace at the right is for a periscope in the wide field mode with line of sight at high elevation.

For the 32 degree field of view and 74 degree elevation angle in this example, remarkably,  viewing at the zenith, +90 degrees, is achieved.

Periscope optics are represented by a single thin lens with entrance pupil located just below the prism.

Real optics would comprise a reversed Galilean telescope, located in front of an objective lens, followed by a series of relay lenses.

The length of the window is determined mainly by the elevation scan range. This is illustrated by the second illustration which is for the same system but in which the line of sight is directed downward to -16 Periscope Window Ray Trace (-16 deg) copydegrees elevation.

The window length is established by the clear aperture required scan to pass the entire field of view at the high and low ends of the line of sight.

The line of sight can be directed to greater angles but vignetting of the field of view then occurs.

A prism is employed in preference to a mirror in order to provide a complete field of view at high elevation angles. By providing  sufficient  window clear aperture by either lengthening or tilting the window  further, a field of view beyond the zenith is possible, a feat which cannot be accomplished with a mirror.

The prism dimensions are determined by the clear apertures of the entrance and exit faces that are required to pass all the light bundles contained within the field of view and, further,  at all elevation angles within the scan range. In this example, both the entrance and exit face minimum sizes are determined by the ray bundle “footprints” at the maximum elevation scan angle.Periscope Prism Aperture HP

In the narrow field of view mode, ray bundle diameters are large and can  govern the prism clear apertures independent of field of view.. This is shown in the ray diagram at the right.

At the zero degrees line of sight prism position,  ray bundles for the full field of view of 8 degrees are well contained within the prism entrance and exit surfaces. At the 40 degrees line of sight position after rotation about the pivot point the bottom end of the prism begins to encroach on the entrance pupil. This results in vignetting of the ray bundles which increases progressively as the line of sight angle is increased.

Window Clear Aperture

The clear aperture of the periscope head window is determined by the ray bundle footprints of the periscope optics in the wide and narrow field of view modes. The aggregate of the footprints on the window surface throughout the entire elevation scan range of the line of sight determines the clear aperture of the surface.. Additional clear aperture is provided as necessary for the window mounting bezel.Head Window Footprint, WFOV copy.

Ray bundle footprints on the outer surface of the window appear at the left for the wide field of view. The field of view is 32 degrees and ray bundle size is 8mm. This footprint pattern comprises the aggregate across the elevation scan range from -16 degrees to +74 degrees line of sight. The +90 and -32 degree footprints are for single ray bundles while all others represent the center of the field of view at various elevation angles accompanied by horizontal fields of view of +/- 16 degrees.

The window clear aperture in this example  is 176 x 60 mm with corners rounded to 30 mm radii.

The window clear aperture for the  narrow field of view is treated similarly. In this instance, however, not all ray bundles can be transmitted without vignetting owing to the larger 42 mm diameter required for the narrow field of view periscope mode.

The ray bundle footprints at the window show the effects of ray bundle clipping from passage through the prism  entrance face, reflection by the  hypotenuse and transmission through the exit face.The tops and bottoms of the pupils at higher elevation angles are lopped flat by the rectangular apertures of the prism. Some clippingHead Window Ray Bundle Footprint, NFOV copy is generally admissible because in direct viewing the exit pupil of the periscope is greater in diameter than the entrance pupil of the viewer’s eye. When imaging sensors replace the eyeball the effect is to reduce the image illumination and in some cases  produce image vignetting.

Ray bundle footprints on the inner surface of the window are similar to those for the outer surface just described. Overall clear aperture dimensions are less due to the refraction at the outer surface and the thickness of the window.

Clear apertures for the rectangular faces of the prism  approach the entire surface areas for the narrow field of view mode. The prism aperture sizes are determined by  simultaneous  consideration of  the narrow and wide fields of view.

Window and Prism Ray Tracing Methods 

Ray Tracing has always been the means to  arrive at  periscope head window and prism design.  In the pre WWII period,  prior to the existence of modern computers with optical design software, ray tracing was done manually by designers who employed a drafting board and tools, and at best  a mechanical desktop calculator to calculate reflection and refraction angles. Ray trace drawings were typically made to a 10x scale on large sheets of paper with fine lead pencils. Many days of iterative ray tracing typically were consumed before a design was completed and only at a fraction of the completeness of a design made with today’s tools. Making out-of-plane ray traces and ray bundle footprint diagrams were not done, these tasks far exceeding  the realm of practicality at that time..

In the late 1960’s, with the advent of the first mainframe computers and  compatible programs, the first significant improvement in ray tracing the head prism and head window was made.  A Fortran program designed specifically to address the head window and prism design problem was written. It permitted a designer to do in hours what previously took days to do and gave the designer the power to explore the impact of the design parameters quickly and easily.  For example, the impact  on prism and window sizes caused by changes to the prism pivot point or entrance pupil locations were quickly and accurately assessed.

Today, modern computer optical design software coupled with a  PC goes a giant step further by allowing the creation of a ray trace model that addresses all the design variables. The model greatly facilitates the study of the impact on prism and window, sizes and clear apertures caused by changes in one or more of the variables.

Ray Trace Computer Model

The ray trace model must consider all the periscope head window and head prism. design variables illustrated in the figure below. Periscope Model Variables

A model which satisfies these requirements has been created using Zemax optical design software. The details of this model and an example of its use appear in the presentation, “Periscope Head Prism and Head Window Ray Trace Model.”







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