Lecture 3: Light Scattering

F. Cichos http://www.uni-leipzig.de/~mona Dynamic Light Scattering - DLS

speckle pattern Dynamic Light Scattering Dynamic Light Scattering - DLS

speckle intensity fluctuations by Brownian motion 100

80

60

intensity 40

0 5 10 15 20 25 30 35 time [s]

3 150x10

) 100

τ

( small q

2

g 50 for Brownian Motion 0 large q

4 6 8 2 4 6 8 2 4 6 8 0.1 1 10 time lag τ [s] Dynamic Light Scattering

slow dynamics - small amplitude motion

fast dynamics - large amplitude motion Lecture 4: Optical Microscopy

F. Cichos http://www.uni-leipzig.de/~mona 2. Optical Microscopy, Computational Microscopy

2.1 Wide Field Microscopy Introduction 2.2 Confocal Microscopy 2.3 Fourier Optics Recapture 2.3.1 Fourier Transform in Optics 2.3.2 Fourier Optics and Imaging with a Lens 2.3.3 Imaging Bandwidth and Resolution

2.4 Phase and Darkfield Contrast 2.4.1 Phase Contrast Microscopy Detail 2.4.2 Darkfield Contrast Microscopy

2.5 Structured Illumination Microscopy

2.6 Photothermal Microscopy 2.7 Superresolution Microscopy 2.7.1 STED microscopy below the diffraction limit 2.7.2 PALM/STORM detection techniques for super-resolution Optical Microscopy

direct imaging raster scanning

bright field microscopy dark field microscopy differential interference contrast micr. confocal microscopy phase contrast microscopy near field microscopy fluorescence microscopy STED microscopy +++ spinning disc microscopy +++ advantages advantages illumination of the whole sample illumination of a small sample volume highly parallel detection from a small sample volume very fast imaging sectioning capability lower background drawbacks drawbacks illumination of the whole sample slow imaging no sectioning capabilities (usually) background fluorescence Near Field Raster Scanning Microscope Wide Field Microscopy Commercial Microscope

key elements

• illumination • imaging optics (objectiv) • tube lens • eye piece/camera

http://www.microscopyu.com/articles/formulas/conjugatemicroscope.html Ray Path through Microscope Wide Field Microscope

microscope intermediate objective image plane

object image

tube lens eye piece

magnification tube lens focal distance (mm)

• tube lens focal distance is typically fixed for Olympus 180 each microscope objective manufacturer Nikon 200 • varying tube lens focal distance leads to new Zeiss 165 magnification Microscope Objective Lens

typical microscope objectives lenses are so called “infinity-corrected” image is created at infinite distance from the objective very useful, because we then have infinite space to place optical elements complex optical system replaced by simple lens picture microscope objective Immersion Fluid

no immersion medium immersion medium Immersion Fluid Widewide fieldField microscope Microscopy

CCD

pro

tube lens • larger excitation volume ø ~10 µm excitation lens filter Δz ~ depends (TIRF)

• parallel acquisition excitation laser dichroic mirror

con • large detection volume • larger background signal microscope • no sample sectioning objective

sample Imaging Small Objects

single PS particle with 600 nm emission

2.0

1.5

1.0

Bildgröße [µm] 0.5 diffraction limit

0.0 0.0 0.5 1.0 1.5 2.0 Partikelgröße [µm]

microscopy image works down to 380 nm Optical Resolution

• point like light source is not imaged into a point!

the image of a point like light source corresponds to the optical impuls response function or point spread function (PSF)

• Fraunhofer diffraction on the aperture of a lens the diffraction pattern is proportional to the square magnitude of the Fourier transform of the aperture function

Fourier transform

example: circular aperture of diameter D Diffraction Limit

resolution = two or one object?

the point spread function (psf) = intensity pattern in the focal area of a lens this is equivalent to the image of a point source (light path is reversible) light is diffracted on the aperture of the microscope objective lens lens aperture pattern is square magnitude of complex amplitude

p(ξ, ρ) = a(ξ, ρ) 2 | |

a(ξ, ρ) is Fourier transform of the aperture (Fraunhofer diffraction)

dimensionless variables 2π 2π ξ(z) = NA2z ρ(r) = NA2r nλ λ

the integrated intensity in every transverse plane is the same Diffraction Pattern

ρresel 0.6 Intensity distribution in the focal plane 0.5 • only true for paraxial optics, but similar for high NA 0.4

0.3 intensity • usually termed resel (resolution element) 0.2

0.1 ρresel is the radius of the so called Airy disc 0.0 -10 -5 0 5 10 ρresel = 1.22π distance in focal plane 1.2 λ r = 0.61 resel NA

0.8

Intensity distribution along the optical axis intensity 0.4

0.0 -40 -20 0 20 40 distance along optical axis Point Spread Function in 3d

the psf is a complicated pattern in 3d space often psf refers to the radial distribution in the focal plane

diffraction changes with wavelength therefore psf too!!!

optical axis focal plane radius

R. H. Webb, Rep. Prog. Phys. 59 (1996) 427. Optical Resolution - Rayleigh Criterium

two psf separated by one resel in plane ρresel 0.6 • dip between the maxima is resolved • dip is 26 % = Rayleigh criterion 26 % 0.4 Rayleigh: two objects can be resolved if λ intensity r = 0.61 0.2 resel NA

338 nm for wavelength 500 nm, NA=0.9 0.0 406 nm for wavelength 600 nm, NA=0.9 -10 -5 0 5 10 15 distance in focal plane

• same can be done along the optical axis

first minimum at this is the axial resolution 2nλ z = axis NA2 about 1.2 µm for 500 nm, NA=0.9 about 1.5 µm for 600 nm, NA=0.9 Diffraction Image

-1000 -500 0 500 1000 x,y [nm] Optical Microscopy - Two Particles

490 nm PS Kugeln Beugungsminimum

-1000 -500 0 500 1000 x,y [nm] 22 %

-500 0 500 x [nm] Abbe Limit - Interference

to find out if there are two light sources in the object plane, one needs to detect the first order interference of the two sources Resolution - Diffraction Limited

Abbe Rayleigh

Ein 1 nm kleines Objekt, dass Licht mit 600 nm emittiert sieht so aus, als wäre er 300 nm groß! Reality and Resolution

same psf but different noise level

0.5

0.3 0.4

0.2 0.3

intensity 0.2 intensity 0.1 0.1

0.0 0.0 -10 0 10 -10 0 10 distance in focal plane distance in focal plane

the resolution criterion is arbitrary, but can be at least exactly determined always hunt for the best signal to noise ratio! special techniques special techniques - dark field microscopy

dark field image of a silicified cell special techniques - phase contrast microscopy

Related Laureate: The Nobel Prize in Physics, 1953 - Frits (Frederik) Zernike » double 1/4 wavelength retardation of the source and the diffracted wave leads to destructive interference in the image plane special techniques - phase contrast microscopy special techniques - phase contrast microscopy special techniques - DIC microscopy

DIC - differential interference contrast special techniques - DIC microscopy special techniques - DIC microscopy special techniques - DIC microscopy special techniques - DIC microscopy Ptychographic Imaging

• high resolution • large field of view Ptychographic Imaging Research Article Vol. 2, No. 10 / October 2015 / Optica 906

(A) phase (0.7 NA) intensity (C) phase intensity 200µm ) × unstained 20µm 20µm conventional 20µm 40 NA, (0.65 20µm phase from defocus from phase

rad

2 stained 20µm 20µm -0.6 20µm 20µm phase contrast (B) with DPC without DPC (D) simulated phase contrast (0.65 NA, 40×)

20µm 20µm FPMsequential FPM source-coded 20µm 20µm 20µm 20µm 20µm -1 2 rad 0 2

Fig. 2. Large-SBP reconstructions of quantitative phase and intensity. (A) Phase reconstruction across the full FOV of a 4× objective with 0.7 NA resolution (sample, U2OS). A zoom-in is shown to the right, with comparison with reconstructions of the same sample before and after staining. (B) Our improved FPM algorithm provides better reconstruction of low-frequency phase information. A zoom-in region shows comparisons between phase reconstructions with and without our DPC initialization scheme. (C) To validate our source-coded FPM results, we compare with images captured with a 40× objective having high resolution (0.65 NA) but a small FOV (sample, MCF10A), as well as with sequential FPM. (D) We simulate a phase- contrast image and compare with one captured by a high-resolution objective (0.65 NA, 40×).

phase information is captured poorly, since it results only from contrast and is nearly invisible; however, the phase result clearly illumination angles that are close to the objective NA. Thus, low- captures the subcellular features. Due to the strong similarity be- spatial-frequency phase information is more difficult to recon- tween the stained intensity and unstained phase, it follows that a struct than high-spatial-frequency phase information, contrary quantitative phase may provide a valid alternative to staining. to the situation for intensity reconstructions. To improve our To demonstrate the importance of using a good initial guess to reconstruction, we use a linearly approximated phase solution initialize the phase recovery for unstained samples, we compare based on DPC deconvolution [25] as a close initial guess for spa- the FPM results both with and without our DPC initialization tial frequencies within the 2 NA bandwidth. We then run a non- scheme [Fig. 2(B)]. Both achieve the same 0.7 NA resolution, linear optimization algorithm to solve the full phase problem (see with high-spatial-frequency features (e.g., nucleus and filopodia) Section 4.B), resulting in high-quality phase reconstructions with being reconstructed clearly, as expected. However, without DPC high resolution [Fig. 2(A)] and good low-spatial-frequency phase initialization, the low-frequency components of the phase are not recovery [Fig. 2(B)]. well recovered, resulting in a high-pass-filtering effect on the re- We demonstrate our new source-coded FPM by reconstruct- constructed phase, much like Zernike phase contrast (PhC). With ing large-SBP videos of popular cell types in vitro on a petri dish, DPC initialization, low frequencies, which describe the overall for both growing and confluent samples. We observe subcellular height and shape of the cells, are recovered correctly. and collective cell dynamics happening on different spatial and Next, we verify the accuracy of the recovered phase values by temporal scales, allowing us to observe rare events in both comparing to images captured directly with a higher-resolution space and time, due to the large space–bandwidth–time product objective (40×, 0.65 NA). The reconstruction resolution for our (SBP-T) and the flexible tradeoff of time and SBP. method matches its expected value (0.7 NA), as shown in Fig. 2(C), which shows images of fixed human mammary epithelial 2. RESULTS (MCF10A) cells. To validate our quantitative phase result, we com- pare with that recovered from a through-focus intensity stack cap- A. Validation with Stained and Unstained Samples tured with the high-resolution objective, and then input into a A major advantage of quantitative phase imaging is that it can phase retrieval algorithm [41] [Fig. 2(C) and Section 4.C]. The visualize transparent samples in a label-free, noninvasive way. quantitative phase can be further used to simulate popular Figure 2(A) compares our reconstructions before and after stain- phase-contrast modes such as differential interference contrast ing, for the same fixed human osteosarcoma epithelial (U2OS) (DIC) and PhC [42]. In Fig. 2(D), we compare an actual PhC im- sample. With staining, the intensity image clearly displays de- age to that simulated from our method’s reconstructed result (see tailed subcellular features. Stained samples also display strong Section 4.D). Since the PhC objective uses annular illumination phase effects, proportional to the local shape and density of the (Ph2, 0.25 NA) to achieve resolution corresponding to 0.9 NA, it sample. Without staining, the intensity image contains very little should have slightly better resolution than our reconstruction. Note Measurement of the Airy Disc

15 µm

Michael Barth. Molecule in Photonic Crystal, POM Lab R. H. Webb, Rep. Prog. Phys. 59 (1996) 427. Single Molecule Defocused Imaging

typically defocusing is unwanted, but it contains information

single DiI molecules in a wide field fluorescence microscope defocused imaging (orientational imaging)

Michael Barth, POM Lab Wide Field Dynamic Imaging

Brownian motion of single dye molecules single CdSe quantum dots

F. Cichos, POM Lab F. Cichos, POM Lab this lecture

2.1 Wide Field Microscopy 2.2 Confocal Microscopy 2.3 Fourier Optics Recapture 2.3.1 Fourier Transform in Optics 2.3.2 Fourier Optics and Imaging with a Lens 2.3.3 Imaging Bandwidth and Resolution

2.4 Phase and Darkfield Contrast 2.4.1 Phase Contrast Microscopy 2.4.2 Darkfield Contrast Microscopy

2.5 Structured Illumination Microscopy

2.6 Photothermal Microscopy 2.7 Superresolution Microscopy 2.7.1 STED microscopy below the diffraction limit 2.7.2 PALM/STORM detection techniques for super-resolution Raster Scanning Microscopy - Confocal Microscopy

• raster scanning microscopy = optical properties are evaluated point wise • sample or the laser beam has to be moved (this makes the hole thing slow)

moving the sample moving the beam sample scanning confocal microscopy laser scanning confocal microscopy optical near field microscopy

100 µm x 100 µm x 20 µm

scanner as used in the POM lab (Physik Instrumente) Confocal Microscopy - Concept

wide field microscopy

• image is sharp in depth of field • other areas unsharp but contribute to background

• pinhole blocks light from unsharp regions (this is a spatial filter) • light from small sample volume is detected

confocal microscopy

• combine this with local illumination

better contrast, slightly higher resolution but at the cost of imaging a point only

Marvin Minsky,1955 patented 1957

first page of the patent (Marvin Minsky)

photo of the confocal microscope prototype 2.4. Microscopy & Near-field Optics 29

4 1.0 2 ] . 0.8 u . a [

ë 0 0.6 y t i 0.4 s

-2 n e

t 0.2 n I -4 0 -4 -2 0 2 4 -4 -2 0 2 4 ë ë (a) Two spots at the diraction (b) line cut limit

Figure 2.13: Two spots in the image plane at the resolution limit of an optical microscope. Two spots can be classified as resolved, if their centers are further apart than the first minimum of the Airy function (see figure 2.12, the minimumtypical is at 1.22 confocal). Following setup this definition,confocal the resolution microscope can be defined as in equation 2.63. The height of the intensity dip in the middle of the structure amounts to 26.5%.

Dichroic Sample Mirror pro • small excitation volume ø 300 nm Δz 500 nm Microscope filter Objective Excitation • small detection volume Pinhole Detection • spatial filtering due to pinhole Pinhole (sectioning capabilities)

con • small excitation volume no parallel data acquisition Detector/APD • imaging by scanning (slow)

Figure 2.14: In this figure the principle setup of a confocal micro- scope is shown. One major component is the pinhole in the detection arm, which allows a higher resolution in the depth of the sample. Objects which are not in the image plane are virtually cut out by the pinhole and do not contribute to the detected signal. In our experiments the small (125µm diameter) detector area of an APD was used as a pinhole in the detection arm. The beam quality of the excitation beam is optimized by the excitation pinhole, in our experiments usually an optical single mode fiber. confocal microscopy - lateral resolution

illumination and imaging is done with the same lens

p (ξ, ρ) = p(ξ, ρ) p(ξ, ρ) confocal psf is a the product of illumination and detection psf ! conf × detection with an infinitely small detector (pinhole) ρresel 0.6 0.6

0.5

0.4 0.4

0.3 intensity intensity 0.2 0.2

0.1

0.0 0.0 -10 -5 0 5 10 -10 -5 0 5 10 15 distance in focal plane distance in focal plane

to obtain a 26 % dip two psf’s are separate by • the psf is narrower than in wide field λ ∆r = 0.44 • fringes are deacreased in intensity conf NA

lateral resolution is 72% of wide field microscopy the squared psf makes the resolution! 500 nm, NA=0.9 gives 244 nm resolution 0.6

0.5

0.4 confocal microscopy0.3 - axial resolution intensity 0.2

0.1

0.0 -10 -5 0 5 10 was only square for wide field microscopy distance in focal plane 1.2 ξ ξ 4 I sin / axis ∝ 4 4 ! ! " ! "" 0.8 nλ ∆zaxis = 1.5 intensity NA2 0.4

about 0.9 µm for 500 nm, NA=0.9

0.0 axial resolution is 75% of wide field microscopy -40 -20 0 20 40 distance along optical axis but goes with

the squared psf makes the resolution of the confocal microscope! the effect of squared psf

Confocal optical microscopy 437 436 R H Webb

wide field psf

Figure 8. p(⇤, ⌥) for the focal plane and planes parallel to it: in (a) this is for the conventional diffraction pattern, and in (b) it is for the confocal case. Figure 7. The point-spread function in through-focus series. Each sub-picture is from a plane parallel to the focal plane. These are actual photographs as a microscope is stepped through focus. Intensity has been manipulated, since the centre of the in-focus panel is really 100 times Point-spread function—Gaussian beam. The concept of numerical aperture and the psf brighter than any of the others. shown above assumes that the pupil of the objective lens limits the light. That means that the illumination overfills the pupil with a uniform irradiance. Laser illumination does not radius, is the Airy disc. The radius of the first dark fringe is meet these criteria. A laser beam has a Gaussian cross section in intensity, and is specified 2 ⇧resel 1.22⌦, (7) by its half or 1/e power points. = or 2⌥2/w2 I (⌥) I0 e , (10) r 0.61⌅/n sin ⌃ . (8) = resel = where w is the parameter describing the beam width, usually called the ‘beam waist’ but I prefer to use the form referring to the beam radius at 1/e2. r 1.22⌅ f/#, (9) If such a beam underfills the lens pupil it will be focused to a beam waist that is Gaussian resel = ⇥ in cross section. A partially filled pupil will produce a mixture of the Gaussian and diffrac- where ⌅⇥ ⌅/n . = tion patterns. Then by underfilling the pupil we can avoid all the complexity of the diffrac- tion pattern and get much more light through, at the cost of a slight decrease in resolution. Figure 9 demonstrates this for pupils uniformly filled (flat) or cutting the Gaussian profile 1 2 at 2 , 1 or 2.5w. A match at the 1/e points—pupil edge at w—loses only 14% of the light and spoils the resolution very little. We generally want to use all the laser light we paid for. the confocal psf in 3d

wide field psf confocal psf

main difference in the lobes gives better contrast

integrated intensity over each integrated intensity over each plane is constant plane is not constant

R. H. Webb, Rep. Prog. Phys. 59 (1996) 427. getting contrast

444 R H Webb

the surpression of the diffraction pattern increases contrast, since dim objects are not obscured by the diffraction fringes

Figure 16. Two points of very different (200:1) remission intensity, are well resolved (4.5 resels). In (a) the conventional view leaves the dimmer point obscured, but in (b) the confocal contrast enhancement allows its display. Arrows indicate the weaker remitter.

So a bright object near a dim one is less likely to contribute background light—to spoil the contrast. In turn, that means that the resolved dim object can be seen as resolved. As an example, figure 16 shows two point objects in the focal plane that are separated by 4.5 resels and differ in brightness (that is, in remission efficiency) by 200. When the diffraction pattern centres on the dim object, for a conventional microscope the dim object is still obscured by the bright one, but in the confocal case both of the resolved points are visible [13]. Another important difference between pconf(⇤, ⌃) and p(⇤, ⌃) is that integrals over the parallel planes (⇤= constant) of pconf(⇤, ⌃) are not equal. In p(⇤, ⌃) every plane parallel to the focal plane is crossed by the same amount of energy, but in the confocal case the function pconf(⇤, ⌃) does not represent an energy at the plane, it describes energy that has reached the plane and then passed the confocal stop—the pinhole. The integral over planes of constant 1 ⇤ for pconf(⇤, ⌃) falls to zero with a half-width of about ⇤ 0.6: p(0.6, ⌃)⌃ d⌃ 2 . Thus planes parallel to the focal plane, but more than ⇤ 0.6=away from the focus, do⇥not contribute obscuring light to the image. These matters have= been discussed⇥ in greater detail by a number of authors [7, 12, 14] . The consequence, then, of confocal detection is that the resolution is less degraded by variations in contrast, and that resolution is slightly improved. The dramatic difference appears when we extend this analysis out of the focal plane.

1.4.2. Axial resolution. The contrast enhancement that discriminates against nearby scatterers in the focal plane becomes dramatic when the obscuring objects are out of that plane. In figure 8(b) there are almost no intensity peaks out of the focal plane. Along the ⇤ ⇤ 4 optic axis equations (20) and (A9) reduce to sin 4 / 4 . Again Rayleigh’s 26% dip will serve to define resolution: ⇤

⌥⇤axresel 0.2 ⌦ 0.6, (23) = ⌅ =⇤ the pinhole resolution and contrast

• the pinhole does not change the psf • the psf is a property of the objective (NA) but the pinhole corresponds to a certain area in the object plane the bigger the pinhole, the more photons will go through it example: 1 mm pinhole corresponds to 10 µm in the object plane for a 100x objective each point light source in the object plane gives rise to a psf in the image plane (pinhole) the detection intensity is a convolution of psf and pinhole

large pinhole blurs the psf

this has o be multiplied by the excitation psf

10 µm a pinhole smaller than 1 resel will not improve resolution it will only reduce detected light effect of the pinhole

despite the large pinhole confocality preserved

R. H. Webb, Rep. Prog. Phys. 59 (1996) 427. the truth

so far the psf was only for paraxial approximation for objective lenses the paraxial approximation is not valid true electric field

θ iξ cos α/ sin2 θ I0(ξ, ρ) = J0(ρ sin α/ sin θ)√cos α sin α(1 + cos α)e dα !0 θ 2 iξ cos α/ sin2 θ I1(ξ, ρ) = J1(ρ sin α/ sin θ)√cos α sin α e dα !0 θ iξ cos α/ sin2 θ I2(ξ, ρ) = J2(ρ sin α/ sin θ)√cos α sin α(1 + cos α)e dα !0

J0, J1, J2 are Bessel function of first kind the real point spread function

three Bessel functions J0, J1, J2

point spread function for a high NA lens 1.0

p(ξ, ρ) = I 2 + 2 I 2 + I 2 {| 0| | 1| | 2| } 0.5 (unpolarized light) 2 ,J 1 ,J

0 confocal psf for a high NA lens J 0.0 p (ξ, ρ) = I 2 + 2 I 2 + I 2 2 conf {| 0| | 1| | 2| }

-0.5 0 10 20 30 40 50 distance

I1(ξ, ρ = 0) = I2(ξ, ρ = 0) = 0 Example Confocal Image

silicon quantum dots

10 µm

J. Martin, POM/OSMP Lab Live Cell Spinning Disk Microscopy 59 Special Techniques - Spinning Disc Confocal Microscopy AB

C

Fig. 1A–C Operating principles of single and multi-beam scanning confocal microscopes: A schematic drawing of a single beam scanning confocal microscope; B schematic drawing of a multi-beam scanning confocal microscope (Yokogawa CSU 10); C the constant pitch helical pinhole pattern of the Yokogawa spinning disk in the image field. During rotation of the disk, the pinholes evenly sweep the whole field of view beam scanning confocal approach was parallelized to utilize multiple beams and corresponding pinholes [1]. Although this approach overcame the severe speed disadvantage of the single beam scanning method, it had significant problems of its own. For fluorescence imaging, the technology suffered from little excitation light reaching the sample due to the limited pinhole area (ap- proximately 1%).Additional drawbacks were the requirement of high precision in the pinhole placement for designs with opposing excitation and emission How to improve the resolution?

lateral resolution of 244 nm is not bad (SNR is important) but axial resolution (0.9 µm) is bad!

nλ axial resolution scales with NA-2 ∆z = 1.5 axis NA2 currently NA=1.6 is the current microscope objective limit, but for n=1.5 simple idea:

use a larger solid angle with two microscope objectives

4pi psf: p(ξ, ρ, φ) = a(ξ, ρ) 2 = a (ξ, ρ, φ) + a (ξ, ρ, φ) 2 4P i | | | 1 2 |

S. Hell and E. H. K. Stelzer, ‘‘Properties of a 4Pi confocal fluorescence microscope,’’ J. Opt. Soc. Am. A 9, 2159–2166 1992. axial resolution - 4pi point spread function

illumination two objective illumination

interference of the two optical fields

sharper main maximum in the middle but two strong side lobes

conf exc det p(ξ, ρ)4P i = p(ξ, ρ)4P i p(ξ, ρ)

image from M. Martinez-Corral, G.I.T. Imaging & Microscopy 2/2002 4pi Confocal Microscopy

4pi excitation - 4pi detection

image from M. Martinez-Corral, G.I.T. Imaging & Microscopy 2/2002