See https://www.researchgate.net/publication/276541892_Optimization_of_Linear_Filtering_Model_to_Predict_Post-LASIK_Corneal_Smoothing_Based_on_Training_Data_Sets

and

http://patents.justia.com/patent/9659151

Article Optimization of Linear Filtering Model to Predict Post-LASIK...

Anatoly, thank you very much for the references.

Can you please briefly explain, what means Linear Filtering Model in this context?

Dmitri,

Linear filter is a mathematical concept. The idea behind the research, which I performed, was to get rid of spherical aberration (SA), which often happens after LASIK. The aberration appears because after the treatment, the cornea epithelium gradually diffuses to the dips, created by LASIK and thus makes cuts smoother. Since the cuts for myopia are mainly on the cornea periphery, this causes SA.

We wanted to find some adjustment the required treatment target to cancel this effect. I realized that any real biological models, based on actual epithelium cells dynamics, will not be accurate enough to provide precision necessary for LASIK. Therefore, I developed a purely empirical mathematical model of after-LASIK epithelium diffusion, which is derived from available post-op data. The model is a linear filter - an operator, applied to the treatment target to account for post-treatment epithelium smoothing. If we want to cancel this smoothing effect and get rid of SA, we need to apply inverse of that operator to the treatment target. Then, when such adjusted target is used for treatment, the result would be the desired corneal shape with no SA.

Dear Anatoly, thank you for explanation, it makes more sense.

Please help me to bring your proposed concept towards practical application.

You saying: linear filter - an operator, applied to the treatment target

What is treatment target? 

Let say if I implement the Linear filter algorithm in C++, 

how output data can be used in femtosecond device during surgery?

how exactly surgery is going to use the data calculated by Linear filter algorithm?

LASIK is supposed to cut a certain profile in the cornea under the flap. This profile we call a treatment target. I believe, the target adjustment is explained  in the paper and patent, which I mentioned earlier.

Dear Anatoly, thank you for answering my questions.

please help to understand what target adjustment is.

Looking at the attached Figure, it is clear, that having pre-op MSRE of patient  and statistical data, we can get A, B and R linear coefficient for equation.

So we can predict SA for patient with certain MSRE value.

Question is how surgeon or femtosecond device can use the predicted SA value to reduce it? What actions should be made during operation to avoid SA?

Is this relevant to defocus of laser beam during operation? depth per pulse?

Is this relevant to a particular area at cornea or retina?