Systems and methods for treatment target deconvolution
Deconvolution systems and methods based on cornea smoothing can be used to obtain an ablation target or treatment shape that does not induce significant high-order aberrations such as spherical aberration. Exemplary ablation targets or treatment shapes can provide a post-operative spherical aberration that is equal to or below a naturally occurring amount of spherical aberration.
1. A method of determining a vision treatment for an eye of a patient, the method comprising:
receiving, at an input, an original target profile for the eye of the patient;
obtaining a spatial domain kernel filter, wherein the spatial domain kernel filter is based on an inverse Fourier transform of a Fourier domain noise filter;
convolving, using a convolution module, the original target profile with the spatial domain kernel filter, wherein the convolving module comprises a processor and a tangible non-transitory computer readable medium, and the computer readable medium is programmed with a computer application that, when executed by the processor, causes the processor to determine a convolved profile based on the original target profile and the spatial domain kernel filter; and
determining the vision treatment based on the convolved profile.
2. The method according to claim 1 , wherein the Fourier domain noise filter is based on a conjugate of a Fourier domain complex matrix.
3. The method according to claim 1 , wherein the Fourier domain noise filter is based on a modulus of a Fourier domain complex matrix.
4. The method according to claim 1 , wherein the Fourier domain noise filter is based on a conjugate of a Fourier domain complex matrix and a modulus of the Fourier domain complex matrix.
5. The method according to claim 1 , wherein the Fourier domain noise filter is characterized by fraction having a numerator comprising a conjugate of a Fourier domain complex matrix and a denominator comprising a modulus of the Fourier domain complex matrix.
6. The method according to claim 5 , wherein the Fourier domain complex matrix is characterized by the formula
K
(
k
x
,
k
y
)
=
1
1
+
σ
2
(
k
x
2
+
k
y
2
)
(
0.5
d
L
)
2
where σ represents a diffusion coefficient, k x and k y represent frequency domain variables, and dL represents a mesh size.
7. The method according to claim 6 , wherein σ has a value of 0.35 mm and dL has a value of 0.1 mm.
8. The method according to claim 6 , wherein σ has a value within a range from about 0.2 mm to about 0.5 mm.
9. The method according to claim 6 , wherein σ has a value within a range from about 0.33 mm to about 0.4 mm.
10. The method according to claim 6 , wherein the denominator is characterized by the expression |K(k x , k y )| n , where n is an integer having a value of 2 or more.
11. The method according to claim 6 , wherein the denominator is characterized by the expression [|K(k x , k y )| n +SNR 2 ] where n is an integer having a value of 2 or more and SNR represents a signal to noise ratio value.
12. The method according to claim 1 , wherein the convolved profile comprises a transition zone radius, the method further comprising zeroing the convolved profile at locations outside of the transition zone radius.
13. The method according to claim 1 , wherein the original target profile comprises an original refractive spherical equivalent value within a 4 mm diameter area, and the convolved target profile comprises a target refractive spherical equivalent value within a 4 mm diameter area, the method further comprising scaling the original refractive spherical equivalent with the target refractive spherical equivalent value.
14. The method according to claim 1 , further comprising elevating the convolved profile so that a lowest point on the convolved profile is zero or greater.
15. The method according to claim 1 , wherein the convolved profile comprises a transition zone radius, the method further comprising applying a damping multiplier at or near the transition zone radius.
16. The method according to claim 1 , wherein the target shape comprises an optical zone having a periphery, and the convolution effects a change in the target shape near the periphery of the optical zone.
17. A system for determining a vision treatment for an eye of a patient, the system comprising:
an input that receives an original target profile for the eye of the patient;
a convolution module comprising a processor and a tangible non-transitory computer readable medium, wherein the computer readable medium is programmed with a computer application that, when executed by the processor, causes the processor to determine a convolved profile by convolving the original target profile with a spatial domain kernel filter to obtain a convolved profile, wherein the spatial domain kernel filter is based on an inverse Fourier transform of a Fourier domain noise filter; and
a treatment module that determines the vision treatment based on the convolved profile.
18. The system according to claim 17 , wherein the Fourier domain noise filter is based on a conjugate of a Fourier domain complex matrix.
19. The system according to claim 17 , wherein the Fourier domain noise filter is based on a modulus of a Fourier domain complex matrix.