Analog Fractal Resampling

[Mustafa Umut Sarac]

I thought some fractal resampling softwares are amazing but extremelly slow. If we can make a filter in front of camera lens , we can increase any lens resolution. I researched the subject and I had had no idea , how that works. I found a paper talking about kerr effect filter and it was diffract a image point spreads in to smaller than the image point , similar to image point images.

one image point painted around with spreading its smaller and smaller copies .

I am not sure kerr effect is works with natural light intensities and I want to know if anyone read such a technology.

ps. I need to indicate , fractal resampling works with not same but similar and going to far and smaller , more basic shapes.

Umut

 

[ntenny]

I don't think resampling algorithms are a very good analogy here, since they depend on having discrete samples. Also, fractal resampling can look very good in practice, but of course cannot create information that doesn't already exist---like other sharpening and resampling techniques, it's basically an illusion that makes the eye see a "better" image even though strictly speaking information is being lost, not gained.

No idea about the Kerr effect. Lasers are above my pay grade.

-NT

 

[Mustafa Umut Sarac]

I read few test articles about fractal resampling and they make blurred image transformed in to very sharp , no blur , no excess contrast , no bandsaw like corner images. Ultra clean and successful. May be diffractive optics have a chance but may be someone , somewhere read something.

Google is a very strange tool, it reveals the information when you asks very strange questions.

 

[Mustafa Umut Sarac]

Analog Fractal Resampling and Optical Feedback

I think I found optical feedback is interesting to generate this technique. I am continueing to research.

 

[Mustafa Umut Sarac]

. FRACTALS IN NONLINEAR CAVITIES
Earlier analyses and simulations of a simple system with a
single Kerr slice and a feedback mirror [13,14] demonstrated
spontaneous nonlinear fractal formation. Our later analyses of
dispersive and absorptive ring cavities [15] provided further
evidence that multi-Turing threshold minima can be a generic
signature of a system’s innate fractal-generating capacity.
A nonlinear Fabry-Pérot cavity is a deceptively simple
system, since it has potential for highly complex behaviours
even in the plane-wave limit [21]. Results of analyses of this
new geometry will be presented. The full transverse system
can be analysed as a direct generalisation of a single feedback
mirror system [13,14], in which one of the faces of the thin
Kerr slice is partially reflecting. Spontaneous pattern
instabilities arise from an interplay that involves: cavity
boundary conditions; diffraction of light beams; diffusion of
the medium excitation (whose optical response gives rise to
nonlinearity); and the interaction of counter-propagating light
beams

 

[Mustafa Umut Sarac]

(i) Linear fractals.One of the earliestreports of linear
optical fractals is diffractals(plane waves scattered by nonregular/fractal objects) [1]. Although it is intuitive that light
diffracted by complex gratings might acquire complex
structure, even a simple (regular) square-wave grating can also
produce fractal light patterns through repeated self-imaging of
the grating itself (the Talbot effect) [2]. Self-imaging is a
property of many linear opticalsystems. For instance, the
transverse empty-cavity modes of classic unstable strip
resonators have fractal character [3], where the eigenvalue
problem (a criterion for self-reproducing mode profiles)
involves an interplay between small-scale diffraction effects at
the mirror edges and successive round-trip magnifications [4].
Mode fractality was later confirmed in so-called kaleidoscope
lasers, that include non-trivial transverse boundary conditions
[5,6]. Alternative schemes for optical self-imaging, such as
multiple-reduction copiers and pixellated video feedback
setups [7], have provided further (potentially linear) contexts
for spatial fractal formation;
(ii) Soliton fractals. A range of fractal patterns in solitonsupporting systems has been identified over the last two
decades. The existence of these patterns is directly related to
nonlinear light–material coupling. Self-similarity has been
predicted during the amplification of parabolic pulses in optical
fibres [8] and also in the distributions of soliton profiles in
systems with series of abrupt material discontinuities (that can
induce individual new scale lengths through splitting
phenomena) [9];
(iii) Nonlinear phase-space fractals.Fractals can appear in
the parameter characterization of nonlinear optical phenomena
(while their real-space and time representations remain nonfractal). Examples include bifurcations in the phase-space of
chaotic pixel-pixel mappings in optical memory applications
[10] and in the properties of interacting vector solitons [11];
(iv) Spontaneous nonlinear spatial fractals.Finiteamplitude simple universal patterns (e.g., stripes, squares,
hexagons, honeycombs, etc.) may grow spontaneously from the
homogeneous states of a reaction-diffusion system that is
sufficiently stressed. Turing showed that the origin of simplepattern emergence is the existence of a singlethreshold
instability minimum whose characteristics dictate the dominant
scale length of the pattern [12]. More recently, we proposed
that any system whose threshold instability spectrum comprises
a hierarchy of comparable Turing minima may be susceptible
to truly spontaneous fractal pattern formation. The first
prediction of such patterns was made for a simple system: the
Kerr slice with a single feedback mirror [13,14]. Our
subsequent analyses of dispersive and absorptive ring cavities
[15] have offered further evidence that multi-Turing threshold
minima can be a generic signatureof a system’s innate fractalgenerating capacity.