
            LES (Lens Evaluation Software version 4.0) Walk-through:

        In DOS, move to the directory where les.exe is located.  Type LES to 
  start the program.  A clear screen with a prompt saying "lensfile:" appears.
  Type in "lenslib", without the quotes, and press enter.  LES accepts upper
  or lower case characters, so you could have typed LENSLIB and it would work
  too.  A screen appears asking about your display and whether you want to
  print.  (Or, from DOS you could start by typing LES LENSLIB and that would
  get you to the display query screen just as well.)
        Enter "C", "E", or "M" at the prompt for screen and printing, and
  you'll see the top level menu for LES.
        LES is controlled by a tree of menus.  Each menu has its name on the
  left side of the menu; you'll see "TOPLEVEL" identifying this first menu.
  Each menu item has the first few letters of a command.  Press "h" (for help)
  and carriage return and a context sensitive (different for each menu) help
  screen will appear, explaining what each command is.
        LES does not have "hot keys"; to execute each menu command, you'll
  have to type a single letter, then carriage return.  From now on in this
  walk-through, when the text says "type x" it really means type x followed by
  a carriage return.
        After the program puts up the help screen, it displays the menu again.
  Type "L", and the lens library menu comes up.  Type "L" and a list of lenses
  in the library comes up.  This list has three columns.  The first is the
  lens name; you'll use this string later to bring the lens up to work with
  it.  There are also columns with the date and time associated with the lens.
  These are there in case you forget the name you saved the lens under, but
  can remember when you last worked on it.
        Type "F" to fetch the lens, and when the prompt "Which Lens?" appears,
  type in "SINGLET".  The program loads the lens into the working area of
  memory, and displays a message that says "Lens SINGLET is ready", and then
  displays the library menu again.  Type "/" to leave the library menu and to
  move up the menu tree to the top level menu.  Type "D" and the describe menu
  appears.  Press "R" and a little table of numbers appears.  This table is
  part of what in the trade is called the "prescription".  (Some people can
  remember the old days when prescriptions were saved on punched cards, so
  prescriptions were called the "lens deck".  If you want to communicate with
  an experienced lens designer, you can use the phrase and impress him with
  your knowledge.)
        LES uses much the same lens representation as other lens analysis
  programs.  Light goes from left to right, starting at surface zero, the
  object surface (more about this surface later).
        In order to perform the refraction calculation correctly for each
  surface, the program needs to have information about the bending (radius of
  curvature) of each lens surface and about the refractive index on either
  side of the surface.  In the trade, this calculation is called the refract
  step.  The program also calculates the ray height where the ray strikes the
  following surface.  This is called the "transfer" calculation, and to do
  this the program has to know the distance traveled.  So the screen you're
  looking at is the heart of the raytrace process because it holds information
  key to both the refract and transfer calculations.
        In the table displayed, the first lens surface is surface 1.  It has
  a radius of curvature of 60.733 units, in this case 60.733 millimeters.  It
  is a positive number, meaning the center of curvature is to the right, i.e.,
  in the positive z direction.  In other words, the first lens surface is
  concave on its right side.  The second surface has a negative radius on it;
  it is concave on its left side.  Thus this lens is fatter in the middle than
  at the edges because both surfaces bend it that way.
        The next column is the curvature, which is the reciprocal of the
  radius.  Lens designers sometimes like to use curvature because it is
  directly proportional to the power of the lens.  Higher curvature surfaces
  bend the ray more (relative to the optical axis along the center of the
  lens) as it refracts.
        New users sometimes get confused and input a radius number into the
  input field for a curvature.  This can cause big problems.  Here's an
  example: a user has a lens with a 100 mm radius of curvature.  They input
  this into the curvature field by mistake.  The program believes it, of
  course, and now it thinks it has a surface with a radius of curvature of
  0.01 mm.  This is tiny!  It means that the surface closes over on itself,
  and rays higher than 0.01 will fly over the surface, because it doesn't go
  that far up!  So when the raytrace tries to intersect the surface, the ray
  will fail.  Moral: after you enter lens radii or curvatures, sit back and
  look at them and see if any very small radius of curvatures show up.  If
  they do, ask yourself "is this really a radius, or did I input a radius into
  the curvature field".  The problem can also occur when someone inputs a
  curvature number into a radius field.  Beware!  If you do much playing with
  lens analysis, you'll do it yourself sooner or later.  Another clue is when
  you get ray failures when you trace real rays (paraxial rays will trace just
  fine, though, and sometimes can help you to see which surface is poisoning
  your lens).  Enough about curvatures; back to the walkthrough.
        The third column shows the spacings in the lens system.  These are
  measured along the optical axis, which is a straight line through the middle
  of both lens surfaces.  The table shows that the lens is 2.751 mm thick, and
  then there is a 98.288 mm airspace to the focal plane.  Surface 3, the last
  surface, is the image surface, and for this lens it's curved inward.
        The fourth column shows the refractive index of the medium to the
  right of each surface.  A ray coming from the right goes into glass as it
  penetrates surface 1, then gets into air again as it comes out through
  surface 2.  If you have a long and complicated lens, scan this column for
  refractive index values greater than 1; that will tell you where each lens
  begins.  In this case, there's only one lens, with an entrance surface
  (surface 1) and an exit surface (surface 2).  The refractive index to the
  right of the image surface is 1.00000, but the program won't use that
  information in a refraction calculation because it stops tracing when a ray
  hits the image surface.
        Enter "P" to see the lens parameters.  The gaussian image height is
  used in paraxial ray traces; this is discussed later.  The entrance pupil
  and aperture stop are related.  The aperture stop limits the size of the
  light beam that goes into the lens. It is sometimes simply called "the
  stop".  There is only one stop per lens system.  This program assumes that
  the stop is a circular (not square) hole.  The image of the aperture stop
  on the object side of the lens is called the "entrance pupil".  For this
  lens, the aperture stop is the first surface, so the aperture stop and the
  entrance pupil are the same surface.  (If you want to learn more about
  stops and pupils, read Jenkins & White's "Fundamentals of Optics",
  published by McGraw Hill).  Since the entrance pupil is an image of the
  stop, a ray through the edge of the stop will also graze the edge of the
  entrance pupil.  This means that we can either specify the size of the stop
  or the entrance pupil.  In this program we use the pupil.  When the computer
  program starts to trace rays, it uses this information to determine how high
  up (or down) on the first lens surface the ray will strike.  In this case,
  the aperture stop is on surface 1.  Sometimes miscommunication about the
  size of something occurs in optics programs that causes an error of a factor
  of two.  For example, note that the opening of the entrance pupil is 5 mm
  radius, or 10 mm diameter.  The same thing happens with the field of view:
  a 60 degree full field of view may be possible, but a 60 degree half field
  of view, which is 120 degrees full, is tough to do.
        The parameters screen shows that the object is at infinity.  This is
  useful for telescopes, binoculars, and for camera lenses looking at distant
  objects.  The program can also handle objects a given distance away, as
  would be the case for a portrait lens or a relay group.  This lens is focal,
  which means it forms an image.  An afocal lens takes a collimated beam in as
  input, and outputs a collimated beam; it does not form an image.  A "tele-
  extender" for a camera lens is afocal.  The lens units for this lens are
  millimeters.
        Type "/" to leave the describe menu and move up to the top level menu.
  Type "A" to choose the analysis menu, then "P" for a paraxial raytrace.  A
  table of values appears.
        Paraxial rays are fictitious rays that use simplified refract and
  transfer equations.  Where the paraxial ray heights are small will
  correspond to where real rays focus, so there's strong correlation to
  reality.  Paraxial rays don't experience aberrations, and that's why real-
  ray raytracing is essential.  There are two paraxial rays of special
  interest: the axial and the chief paraxial rays.
        The axial ray is a ray from the base of the object to the top of the
  pupil.  When the object is far away, the slope is small; when the object is
  at infinity, the slope is zero.  This is the case here.  The ray coordinate
  is 5mm on surface 1, which is correct since surface 1 is the stop and the
  entrance pupil.  The slope after surface 1 is -0.042705; the minus sign
  means the ray has been bent down, as we would expect.  After surface 2, it
  is bent even more to give a slope of -.05, and on surface 3, the image, the
  height is very small.  This is also to be expected, since the lens should
  form an image of the foot of the object at the middle of the focal surface.
        The chief ray is a ray from the top of the object through the center
  of the stop.  Since for this lens the object is at infinity, the object
  height is undefined.  The program puts a zero value into the Y-height for
  surface 0.  The Y-height on surface 1 is really 0, since the ray by
  definition goes through the center of the stop.
        The effective focal length (EFL) of the lens, often called just "the
  focal length", is shown to be 100 mm, and the back focal length (BFL) is
  98.453.  The EFL is the distance from the principal plane to the image
  plane, while the BFL is the distance from the last lens surface to the
  image plane.  For a discussion of principal planes, see Jenkins & White, or
  an elementary optics text.  The f/number is 10.  Press "C" to see a surface-
  by-surface raytrace of a single ray.  Enter "F" to allow ray input in terms
  of angle, then type "0 5" and carriage return.  The two integers can be
  separated by one or more spaces.  A table appears containing data from a
  real-ray raytrace.  The z coordinate is the distance in the direction of the
  optical axis, displaced from the tangent plane to the surface.  The X
  dimension is the horizontal distance from the vertex, and the Y dimension
  is the vertical distance.  This raytrace tells that a "gut" ray from 5
  degrees off-axis will strike the image plane 8.646888 mm above the center
  of the image plane.
        Enter "S" for a spot diagram, then "26" for the number of rays.
  Input "F" to choose degrees as the mode of field angle input, then "0 5" and
  enter.  A screen of data appears giving statistics on the ensemble of rays
  that compose the spot diagram.  Press the space bar to see a plot of the
  spot diagram, then press it again to clear the plot and return to the
  analysis menu.
        Press "/" to leave the analysis menu and move to the top level menu.
  Press "Q" to quit; type in "N" to exit completely.
