Nick Beavers Project Manager Deconvolution from Andy Molnar Software Engineer

Basics of Fluorescent Imaging

What is Fluorescence Imaging? Unlike reflection or absorption imaging. Use molecules called fluorophores: –Upon illumination by light of a specific wavelength they emit light of longer wavelengths. Absorption (Excitation) Spectrum Emission Spectrum Wavelength Stokes Shift

Lens Light Source Digital Camera Emission Filter Excitation Filter Dichromatic Mirror Objective Lens Fluorescence Microscopy

Microscope Slide Specimen Objective Lens Coverslip Immersion Medium Slide

Fluorescence Microscopy Microscope Slide Specimen Coverslip Slide The Object: A collection of fluorophores small enough to be considered point sources of light.

Image Formation The Object (reality) The Image (reality observed) XY XZ XY XZ What Happened?

Aperture Diffraction

One Dimension - Diffraction Aperature d Point Source of Light

Two Dimensions - Airy Disk

PSF (Point Spread Function) Point in object  Point Spread Function (PSF) in image. –The image is built out of PSFs, not points. Effect of PSF –Features blur together –Measurements are corrupted Deconvolution –Undo effect of PSF

Resolution and Blur

Effect of the PSF Object -> Image

PSF in 3 Dimensions In 3d Widefield, light from out of focus planes is detected in focal planes. In Confocal, pinholes help but there is still some z-blur especially when SA is present. XY XZ WidefieldConfocal XY XZ

The Problem How to make a measured image better represent the real object ? 1)Counteract the PSF – that is put the light that spread (Airy disk) out back to its 2D location 2) Put light into the proper Z plane 3) Reduce the noise This is best accomplished using deconvolution

Deconvolution of Fluorescence Images

Why Deconvolution? Increased Resolution Better Contrast Improved Signal-to-Noise Ratio

Noise Random nature of Photon Emission –Poission Noise –Usually dominant –Low light levels Digital Imaging System –Gaussian Noise

Noise

Widefield Example Max Projections

Confocal Example

Deconvolution Methods DECON METHOD FEATURE SpeedSubtractive Quantitative Requires PSF Produces PSF S/NNoise No/Nearest Neighbor FastYesNo LowerHigher Inverse FilterModerateNo Higher Non-Blind Constrained Iterative * Mod-LongNoYesYes/NoNoHigherLower Blind Constrained Iterative * LongNoYesNoYesHigherLowest * Can use measured or theoretical PSF

Imaging Equation Mathematical operation called a convolution. The Microscope is a convolution operator. The inverse of a convolution is deconvolution  = Object convolved with the PSF equals the Image ImagePSFObject

Iterative Non-Blind Deconvolution Object EstimateImage PSF Image Estimate Error Update - First Iteration (Fixed PSF)

Blind Deconvolution Object EstimateImage PSF Image Estimate Error Update - First Stage - Image (Adaptive PSF)

Blind Deconvolution Object EstimateImage PSF Image Estimate Error Update - Second Stage - PSF (Adaptive PSF)

Benefits –Can adapt to imperfections in the Microscope. –Double optimization: Object and PSF are modified –Can adapt to changes in refractive index, specimen, environment. –Handles SA well. –No need to measure the PSF. –The only certain benefit of non-blind over blind is that it is faster. Benefits of Blind Deconvolution (Adaptive PSF)

Comparison Original ImageNearest Neighbors Inverse FilterIterative

2D Widefield Example

Example: Slice View slice 29 slice 37 rawdeblurred

The Point Spread Function (PSF)

Determining the PSF Need a input PSF for Inverse filter Constrained Iterative Statistical. Need PSF “first guess” for Blind

PSF - Widefield vs. Confocal XY XZ WidefieldConfocal XY XZ

What effects the shape of PSF?? Lens parameters Modality Specimen Parameters XY XZ Widefield XY XZ Confocal

Spherical Aberration Caused by –Changes in refractive index –Thick specimens –Incorrect cover slip thickness –Worse deeper in the sample Solve by –Match RI –SA correction collar –Use biased PSF and deconvolution

Spherical Aberration

PSF Theoretical Measured Blind

Theoretical –Scope Properties NA, Lens RI, Pixel Spacing, Emissive Wavelength, –Specimen properties Specimen RI, Distance from Coverslip

Measured Bead Image Must be taken under the same conditions as the real sample will be. –Same embedding RI –Same distance from coverslip

Bead Image

Blind PSF PSF also changes as part of optimization Blind: 2 step process in Autoquant –Spherical Aberration Detection –PSF modified further as part of Deconvolution Determine PSF without measuring it.

PSF Comparison MeasuredTheoreticalBlind

Example What happens if you use the wrong PSF??

Raw Image max = 2,614 XY XZ

Deconvolved no SA max = 12,134 XY XZ

Deconvolution with SA Correction max = 23,938 XY XZ

Geometric Distortion With SA PSF changes with depth Actual focus location also changes (PSF Asymmetry) Images look stretched. Scale in Z Many papers on this (Model 2010)

Deconvolution of Confocal Images Yes Confocal images can be deconvolved Confocal images –some blur. –noisy Accurate statistical model is important Poisson model Deconvolution reduces both blur and noise Improves the Signal to Noise Ratio. Multi-Photon, Spinning Disc, Structured Illumination.

Confocal Examples

Collecting Optical Sections Setting the top and bottom of the scan Use Nyquist sampling –Sampling rate needed to collect all information Don’t break rules for convenience only out of necessity

ImagingApproach First try Widefield + deconvolution –Better for low light levels –Living cells –Proteins Next Confocal + deconvolution –Thick specimens (Tissues) Multiphoton + deconvolution –Very thick specimens

Deconvolution Tips Check the image stack’s metadata before decon. Use the line profile to prove that decon works. Use statistics to show… –Average image intensity remain relatively the same –Max pixel intensity can increase by 100 times.

Deconvolution Tips 99% of the time Blind is best. Severe spherical aberration correction is best done by CGC on the objective. Use an AOI for SAC testing or decon testing. AutoQuant 30 Day trial program: –Use it to your advantage! –Customers receive the entire product to evaluate.

Q&A Questions?

Nick Beavers Project Manager Deconvolution from Andy Molnar Software Engineer