Caltar II-N f4.5 75mm Lens - no light falloff?

I'd like to get some of these lenses. Can you please point
us toward them?

Kingslake says of the cos^4 law, "This law operates in all
lenses..." He does go on to mention that some lenses (he
names the Biogon) or "any reversed telephoto lens" (these
include wide angle lenses with will
give more illumination than predicted by the cos^4 law.
He does not mention any lenses with more illumination
in the corners than in the center. I'm just curious here...


"BC" apparently said:

Light falloff is not a theoretical inevitability. In fact, there are
wide angle lenses with zero rectilinear distortion which actually have
slightly *more* illumination in the corners than in the center of the
image.

I'd like to get some of these lenses. Can you please point
us toward them?

Kingslake says of the cos^4 law, "This law operates in all
lenses..." He does go on to mention that some lenses (he
names the Biogon) or "any reversed telephoto lens" (these
include wide angle lenses with will
give more illumination than predicted by the cos^4 law.
He does not mention any lenses with more illumination
in the corners than in the center. I'm just curious here...


"BC" apparently said:

Light falloff is not a theoretical inevitability. In fact, there are
wide angle lenses with zero rectilinear distortion which actually have
slightly *more* illumination in the corners than in the center of the
image.

"I am not sure where you got this knowledge from.
If you take any lens, the projected profile of itself acting as
apterure
changes with the lateral distance from the optical axis. Ad extremum,
if
you consider a point in the infinity away from the optical axis, you do

see nothing more than a line with not opening, right?
Can you please email me at least one quote from an academic book on
optics, which states that the cos^4 law is a meaningless rule of thumb.

I would appreciate to receive it to understand what you mean.
If you feel that this conversation exceeds the framework of this forum,

you are most welcome to email me your response to my email address.
George
PS: The mechanical vignetting is a different pair of shoes...."

I got my knowledge mainly from 20+ years of experience as a
professional lens designer. A close reading of any good optics
textbook (such as Smith) will reveal that the cos^4 "law" depends on
the chief ray angle in image space being equal to its value in object
space, and on the shape and size of the exit pupil being constant with
field angle. These conditions are approximately met by many but by no
means all photographic lenses. Some lenses with commercial value do in
fact violate these conditions to an extreme degree.

Thus, for example, it is possible to design a 100 degree FFOV lens
having essentially zero rectilinear distortion and zero falloff. If
the lens obeyed the cos^4 rule, then the illumination in the corners
would only be about 17% the value in the center. The large difference
between 17% and 100% in this case would fully justifies calling the
cos^4 rule a meaningless rule of thumb, wouldn't you agree?
Brian
www.caldwellphotographic.com

"I am not sure where you got this knowledge from.
If you take any lens, the projected profile of itself acting as
apterure
changes with the lateral distance from the optical axis. Ad extremum,
if
you consider a point in the infinity away from the optical axis, you do

see nothing more than a line with not opening, right?
Can you please email me at least one quote from an academic book on
optics, which states that the cos^4 law is a meaningless rule of thumb.

I would appreciate to receive it to understand what you mean.
If you feel that this conversation exceeds the framework of this forum,

you are most welcome to email me your response to my email address.
George
PS: The mechanical vignetting is a different pair of shoes...."

I got my knowledge mainly from 20+ years of experience as a
professional lens designer. A close reading of any good optics
textbook (such as Smith) will reveal that the cos^4 "law" depends on
the chief ray angle in image space being equal to its value in object
space, and on the shape and size of the exit pupil being constant with
field angle. These conditions are approximately met by many but by no
means all photographic lenses. Some lenses with commercial value do in
fact violate these conditions to an extreme degree.

Thus, for example, it is possible to design a 100 degree FFOV lens
having essentially zero rectilinear distortion and zero falloff. If
the lens obeyed the cos^4 rule, then the illumination in the corners
would only be about 17% the value in the center. The large difference
between 17% and 100% in this case would fully justifies calling the
cos^4 rule a meaningless rule of thumb, wouldn't you agree?
Brian
www.caldwellphotographic.com

The simple two-element example shown in the link below covers 90
degrees with no distortion and with about 6% more illumination in the
corners than in the center. Telecentric lenses for DMD and LCD
projectors are more complicated due to a need for color correction, but
they sometimes have similar illumination properties. A year ago I
designed a wide angle projection lens for an HDTV cinema application,
and this lens does have slightly elevated corner illumination relative
to the center. I can tell you this lens is in a semi-permanent
installation in Las Vegas, but can't say anything more than that. If
you have an application that warrants a custom lens, then email me.

Your Kingslake reference doesn't seem self consistent. Perhaps
something has been left out?

http://caldwellphotographic.com/ILLUM.jpg
Brian
www.caldwellphotographic.com

The simple two-element example shown in the link below covers 90
degrees with no distortion and with about 6% more illumination in the
corners than in the center. Telecentric lenses for DMD and LCD
projectors are more complicated due to a need for color correction, but
they sometimes have similar illumination properties. A year ago I
designed a wide angle projection lens for an HDTV cinema application,
and this lens does have slightly elevated corner illumination relative
to the center. I can tell you this lens is in a semi-permanent
installation in Las Vegas, but can't say anything more than that. If
you have an application that warrants a custom lens, then email me.

Your Kingslake reference doesn't seem self consistent. Perhaps
something has been left out?

http://caldwellphotographic.com/ILLUM.jpg
Brian
www.caldwellphotographic.com

What you write is interesting - can you name one photographic lens which
comes from either Zeiss, Leica, Rodenstock(Linos),
Schneider-Kreuznach, Nikon, Olympus or Kodak which behaves as you describe.
I am probably able to get the lens design for that lens to
verify/confirm your statement.
George



BC wrote:
"I am not sure where you got this knowledge from.
If you take any lens, the projected profile of itself acting as
apterure
changes with the lateral distance from the optical axis. Ad extremum,
if
you consider a point in the infinity away from the optical axis, you do

see nothing more than a line with not opening, right?
Can you please email me at least one quote from an academic book on
optics, which states that the cos^4 law is a meaningless rule of thumb.

I would appreciate to receive it to understand what you mean.
If you feel that this conversation exceeds the framework of this forum,

you are most welcome to email me your response to my email address.
George
PS: The mechanical vignetting is a different pair of shoes...."

I got my knowledge mainly from 20+ years of experience as a
professional lens designer. A close reading of any good optics
textbook (such as Smith) will reveal that the cos^4 "law" depends on
the chief ray angle in image space being equal to its value in object
space, and on the shape and size of the exit pupil being constant with
field angle. These conditions are approximately met by many but by no
means all photographic lenses. Some lenses with commercial value do in
fact violate these conditions to an extreme degree.

Thus, for example, it is possible to design a 100 degree FFOV lens
having essentially zero rectilinear distortion and zero falloff. If
the lens obeyed the cos^4 rule, then the illumination in the corners
would only be about 17% the value in the center. The large difference
between 17% and 100% in this case would fully justifies calling the
cos^4 rule a meaningless rule of thumb, wouldn't you agree?
Brian
www.caldwellphotographic.com

BC wrote:
"I believe the Caltar is the same as my Rodenstock. I haven't checked
Rodenstock's website recently, but if I remember correctly, this
particular lens follows a cos^3 law rather than a cos^4 law, and that
is
possible to achieve by lens design. But to say it has no fall-off is
nonsense."

You have misread my post.

It is not a big deal, but I didn't miss your point. Perhaps I stated it
awkwardly. I just wanted in this case to reiterate that, for the
specific Clatar lens that the question was asked about, there is
significant fall-off and to state otherwise is nonsese.

Do you have a reference about unconventional designs with little or no
fall-off? I imagine there are some other trade-offs, and it would be
interesting to find out more about it.

I never said that the Caltar lens in
question has no falloff. Inverse triplet type lenses of this sort do
in fact tend to have an approximately cos^3 falloff pattern as you
mention. My point was that falloff in general is not always
inevitable, and that it is possible to design and build a
distortion-free wide angle lens which has greater illumination in the
corners than in the center. I don't know what the ultimate limits are,
but I do know for certain that in practice an illumination "gain" on
the order of cos^(-0.1) is possible.

BC wrote:
The simple two-element example shown in the link below covers 90
degrees with no distortion and with about 6% more illumination in the
corners than in the center. Telecentric lenses for DMD and LCD
projectors are more complicated due to a need for color correction, but
they sometimes have similar illumination properties. A year ago I
designed a wide angle projection lens for an HDTV cinema application,
and this lens does have slightly elevated corner illumination relative
to the center. I can tell you this lens is in a semi-permanent
installation in Las Vegas, but can't say anything more than that. If
you have an application that warrants a custom lens, then email me.

The diagram of the lens seems to indicate that one of the elements has a
parabolic rather than spherical form. Is that correct?


Your Kingslake reference doesn't seem self consistent. Perhaps
something has been left out?

http://caldwellphotographic.com/ILLUM.jpg
Brian
www.caldwellphotographic.com

In this particular design all four surfaces are simple conic sections,
but none are parabolic. In the first element both surfaces are
ellipsoids, and function mainly to correct distortion. In the second
element both surfaces are hyperboloids, and function mainly to correct
spherical aberration and coma.

Brian
www.caldwellphotographic.com