OP: Wavefront Aberrometry 2 - Week 5 Flashcards
What is Fourier Transform?
A means of transforming a signal defined in the spatial (or time) domain to the spatial frequency (or temporal frequency) domain
Why might the snellen chart not be the best representation of real word day to day vision?
Snellen charts are high contrast. But much of our world is low contrast
What should we use to test perception of real-world (low contrast) images?
Gratings
What are the benefits of gratings for visual perception testing?
- avoids complications of having to be familiar with letters (e.g. illiterate, foreign)
- can apply fourier transform to images/gratings
How can we mathematically describe the contrast of sine wave gratings?
Use Michelson’s contrast
- which is the difference between the highest and lowest luminance divided by the sum of the highest and lowest luminance
What are the 3 different definitions of contrast, and when are they used?
- Weber Contrast (Cw) - used for isolated features against a larger background (e.g. spot on screen or letter on chart)
- Michelson Contrast (Cm) - used for repeating patterns, e.g. sine or square wave gratings
- RMS (root mean square) Contrast (Crms) - used for more complex patterns (e.g. random dot patterns, natural images)
What is the formula for Weber Contrast?
deltaL/L
i.e. (Ltarget - Lbackground)/Lbackground
What is the formula for Michelson’s Contrast?
(Lmax - Lmin)/(Lmax + Lmin)
What is another way to mathematically define contrast of a grating?
Contrast = Amplitude/mean
How does spatial frequency relate to the period of the grating?
Inverse relationship. SF = 1/period
How can we compute the Point Spread Function?
Through the pupil transmittance function multiplied by the wavefront
- The PSF is the fourier transform of the pupil function
List 3 applications of the fourier transform
- compute the MTF of a wavefront
- compute the PSF from the wavefront
- compute a ‘convolution’ to predict what images look like as viewed through an optical system
What does the Modulation Transfer Function (MTF) do?
It talks about how much the contrast (from 100%) has been attenuated on passage through an optical system
i.e. indicates the ability of an optical system to reproduce various levels of detail (spatial frequencies) from object to image
MTF: How much is image contrast reduced for an object of low spatial frequency?
contrast in image is a little bit lower than object contrast
MTF: How much is image contrast reduced for an object of high spatial frequency?
Contrast drops a lot!
How well do low spatial frequencies pass through an optical system compared to high spatial frequencies?
Low SFs pass through much easier
An ideal pupil of 4mm should be able to see images of 100 cycles/degree. Why can’t real eyes do this?
b/c of aberrations
How does pupil size influence the MTF?
MTF increases with increasing pupil size
How does dioptric defocus effect MTF?
MTF decreases at more than normal at higher SFs when blur is present
What happens to the MTF when you have 0.5 or more diopters of blur?
You start getting negative contrast numbers for higher SFs. This means you actually get a REVERSE IN POLARITY: light regions become dark and vice-versa!
Can the area under MTF be used as an image quality metric?
Yes, though it’s not used much in the clinic, more for research.
What is the phase transfer function?
It relates to how much your optical system changes the phase of your initial object
How much does the phase shift for a low SF object?
Shifts a little bit
How much does the phase shift for a high SF object?
Shifts a lot
What is the Optical Transfer function
OTF = MTF and PTF
So it’s the modulation and phase transfer functions combined into one concept
What is a wavefront?
a locus of points at equal phase
What type of wavefront should a parallel beam produce? What about a converging beam?
parallel: plane wavefront
converging: spherical wavefront
How can we describe the phase of a wavefront relative to an ideal wavefront?
As “advanced-phase” or “lagging-phase”
What units is wavefront error generally measured in?
micrometres
How can we decompose and analyse a wavefront aberration map to make it easier to understand?
Break it down into individual Zernike polynomials, and their relative contributions
What sort of aberrations can we correct in the clinic (using our standard clinic tools)?
Lower order aberrations - i.e. de-focus and astigmatism
What is the principle behind the lenslet array on a Shack-Hartman Wavefront Sensor?
Light coming from a single point on the fovea will go through these lenslet arrays and form a spot of light at the back focal point for each lenslet. If the wavefront coming from the eye is flat (perfect eye): each point of light will be directly aligned with its lenslet.
This means that the shape of the lenslet array will be perfectly geometrically replicated.
Describe the lenslet array itself. How are the lenslets positioned?
Typically a 5-5 square array of lenslets, but could be any shape. The lenslets are all identical, meaning they share the same focal length. Additionally, the lenslets are equidistant to each other. (i.e. same distance apart)
- therefore, in a perfect eye, you the spots of light past the lenslets should also be equidistant to each other
How does variation in the wavefront affect the projection of light that has gone through the lenslets in a Hartman-Shack wavefront sensor, and what would the resulting photograph look like?
“The displacement of each focal spot away from where it ought to be is proportional to the local slope of the wavefront”.
In an aberrated wavefront, spots will NOT be equidistant, and some spots may be brighter or darker than others
What is the purpose of the defocus trombone in the hartman-shack wavefront sensor?
Allows us to correct for simple defocus by increasing or decreasing the entire distance between the object and image
Where do you place the camera in a hartman-shack wavefront sensor?
At the back focal point of the lenslet array
What sort of light do we use for the hartman-shack wavefront sensor?
long wavelength light (often even infrared)
Can hartman-shack images be used for determining refraction?
Mathematically, Yes. But we mainly use this information for a more specialised understanding of refractive error, rather than for day to day
How fast can a computer generate corresponding wave front maps from shack-hartman images?
In an instant
In what manner have wavefront sensor images been particularly useful?
In analysing the refractive results of corneal refractive surgery, e.g. radial keratotomy (RK), (note: that RK is no longer used)
Also useful in deciding on types of contact lenses for Keratoconus
Can you use wavefront information to predict the PSF?
Yes
Compare the PSF of an RK patient vs LASIK patient after their respective operations
RK: Very lobulated (point gets imaged to a lot of tiny dots), but less spread compared to lasik
Lasik: broader PSF but not lobulated.
Which PSF might be better between RK and Lasik patient? Explain
Lasik is possibly better. Because RK is lobulated which could be deleterious for trying to pick out fine-detailed info
What is the advantage of the Root Mean Square?
You can include or exclude any aberration term you want, allowing you to look specifically at certain types of aberration
What are the components of the fourier transform of the PSF?
Amplitude component: MTF
Phase component: PF
What is a zero order aberration? Does it affect vision?
is called a “piston”. This is where the aberrated wavefront is simply retarded or advanced relative to the perfect wavefront. This does NOT impact vision
How would you describe aberrations in the eye. Are they specific or random?
For the most part, they are random
What type of aberrations dominant the higher order aberrations?
Higher order aberrations are dominated by 3rd order (coma and trefoil) and 4th order (spherical) aberrations
What is convolution?
Basically means that every point on an image has its own PSF, and the PSF of the overall image is the sum of the individual PSFs.
This means that individual spread PSFs can accumulate to create a blurry image. (because the individual blurs are being summed)
How does aperture size affect the level of aberrations?
Smaller aperture means less aberrations (including higher order ones)
What factors causes dynamic changes in the wave aberrations? [4]
- accommodation
- eye movement
- eye translation
- tear film
