Cascaded OTFs ?
" >
I am trying to find a reference describing the necessary conditions for
modelling a chain of optical components by cascading (multiplying) the
individual OTFs for each component. Google-ing turned up a couple of
skimpy references, including a photographic lens tutorial that states that
"... the MTFs of cascaded ordinary lenses can legitimately be multiplied
only when a set of quite restrictive and technical conditions is satisfied."
I am looking for a summary of these conditions for incoherent imaging.
Any pointers to web sites, literature etc. would be much appreciated!
TIA,
Hal
Phil Hobbs
Google backwards in this group to last November. We had a quite
spirited discussion of this,
<http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&oe=UTF-8&threadm=vqfmthps9i7he2%40corp.supernews.com&rnum=1&prev=/groups%3Fq%3Dhobbs%2BOTF%26hl%3Den%26lr%3D%26ie%3DUTF-8%26oe%3DUTF-8%26selm%3Dvqfmthps9i7he2%2540corp.supernews.com%26rnum%3D1>
The basic issue is that two phase perturbations (e.g. moving the object
and moving the image to compensate) may have very ugly OTFs
individually, but still cancel out to give a good image. Just
multiplying the two ugly OTFs would give you the wrong answer. If
there's a phase randomizer (e.g. a ground glass plate, an image
intensifier, or something like that) in between the OTFs, then they
multiply fine. Otherwise not.
Cheers,
Phil Hobbs
Repeating Rifle
""harry.ingleby"@nospamrmc.ca"> wrote on 3/18/04 11:04 AM:
What am I missing? If we are talking paraxial linear passive optics. a
device can be represented as a complex transfer function. That is, an input
with spatial spectrum F(wx,wy) entering the system turns into F(wx,wy)
T(wx,wy) where wx and wy are the spatial frequencies and T is the transfer
function. How is the complication introduced?
Bill
Helpful person
You can never "cascade" individual OTF's (which contain both amplitude
and phase information) of lenses. To illustrate this, consider a well
corrected lens system. Split it into two parts, each part by itself
having poor imagery. If the only information you have is the OTF of
the individual parts you cannot determine the performance of the
whole.
If two parts of a lens system are decoupled then one can determine the
overall MTF by multiplying the individual MTFs together. An example
of this is when a scattering screen is placed at an intermediate image
between two parts of an optical system.
Ralph Willoughby
"Helpful person" <rrl...@yahoo.com> wrote in message
news:87946313.04031...@posting.google.com...
> >
> You can never "cascade" individual OTF's (which contain both amplitude
> and phase information) of lenses. To illustrate this, consider a well
> corrected lens system. Split it into two parts, each part by itself
> having poor imagery. If the only information you have is the OTF of
> the individual parts you cannot determine the performance of the
> whole.
>
> If two parts of a lens system are decoupled then one can determine the
> overall MTF by multiplying the individual MTFs together. An example
> of this is when a scattering screen is placed at an intermediate image
> between two parts of an optical system.
Please remind me of the definition of OTF vs MTF.
If the OTF contains both amplitude and phase I am tempted to see it as a
complex quantity, i.e. the straight Fourier transform of the *amplitude*
PSF, but is this not the complex amplitude distribution over the pupil?
Whereas the MTF is a real quantity associated somehow with the *intensity*
PSF.
OK, I am confused, someone please help.
Helpful person
> "Helpful person" <rrl...@yahoo.com> wrote in message
> news:87946313.04031...@posting.google.com...
>
>
>
> If the OTF contains both amplitude and phase I am tempted to see it as a
> complex quantity, i.e. the straight Fourier transform of the *amplitude*
> PSF, but is this not the complex amplitude distribution over the pupil?
>
> Whereas the MTF is a real quantity associated somehow with the *intensity*
> PSF.
>
> OK, I am confused, someone please help.
OTF stands for Optical Transfer Function and is a complex function
containing both real and imaginary parts.
MTF stands for Modulation Transfer Function and is usually defined as
the real part of the OTF.
Raybender
Basically, you cannot cascade, figure out what to do, etc with respect to
Optical system MTF or OTF *until* you reach a square law (intensity) detector in
the system. As noted by others, below, this is because the aberrations
(wavefront phase perturbations) in the lenses add as the light propagates
through the system. The OTF and MTF *only* become defined once you reach the
final point where there is an *intensity* detector, and then they are defined
with respect to the exit pupil function of the *entire* optical system that the
light has passed through before reaching this detector. At *that point* you
must determine whether the system is coherent, incoherent, or partially coherent
(based upon the pupil fill factor from the source) and now compute the
appropriate OTF (coherent, or incoherent)
The MTF's (or OTF's) only cascade when *multiple* systems (lenses) with
intensity detectors *between them* are involved - for example, the MTF of a
camera lens (first detector is the film) cascades with the MTF of the enlarger
lens (first film image is used as input to second system) that has a second
intensity detector (enlarger print film). If you took the film out of the
camera, and then placed the image plane of the camera at the input to the
enlarger (so the camera image essentially is *projected* into the enlarger
optics) you have now created a new *single* optical system with only one MTF
that is completely different from the product of the cascaded MTF's of the
previous *two* optical systems.
Hope this helps.
Frank
Carl G.
The MTF is the magnitude of the OTF. A related, but not often used,
term is PTF, which is the Phase Transfer Function, and is the phase
angle of the OTF.
Carl G.
West Coast Engineering
Fact is, you hit it right on the head and your answer is 100% correct.
Now watch how many people here won't believe you. :-)
They must be ZEMAX users or managers or systems engineers.
WCE