BASICS IN LIGHT MICROSCOPY INTERNAL COURSE 2015 26 TH JANUARY
OVERVIEW Light microscopy Why do we need it? How does it work? What are its limitations? What do we need to consider? - 2 -
HUMAN EYE Normal viewing distance - 250 mm Angular resolution a min 1 Spatial resolution h min 80 mm Nodal distance -17 mm Average retinal cell distance 1.5 mm Spectral range 400 nm - 800 nm Can resolve contrast about 5% High dynamic range 10 decades Max sensitivity at 505 nm (night, rods) Max sensitivity at 555 nm (day, cones) More sensitive to color than to intensity Most perfect sensor for light detection up to now - 3 -
MAIN ISSUES OF MICROSCOPY low contrast low resolution low magnification - 4 -
MAIN ISSUES OF MICROSCOPY Contrast Magnification Resolution Only fulfillment of these three conditions allows translation of information as accurately as possible from object into an image which represents that object. - 5 -
HOW DOES IT WORK? Physical Principles - 6 -
GEOMETRICAL OPTICS THIN LENS Principal plane Focal length f optical axis Focal point Characterization of a lens: Focal length: f=50 mm=0.05 m Power: 1/f =20 m -1 = 20 dioptre - 7 -
GEOMETRICAL OPTICS THIN LENS Principal plane Focal length f optical axis Focal point Working principle of lenses: Refraction Curvature - 8 -
LENS MAKER FORMULA curvature r 2 1 f = n 1 n m 1 1 r 1 1 r 2 focal point curvature r1 focal length Factors that determine the focal length of a lens index of refraction index of refraction of the medium radius of the front surface radius of the back surface Material Index Vacuum 1.00000 Air at STP 1.00029 Water at 20 C 1.33 Fluorite 1.433 Fused quartz 1.46 Glycerine 1.473 Typical crown glass 1.52 Crown glasses 1.52-1.62 Material Index Flint glasses 1.57-1.75 Heavy flint glass 1.65 Sapphire 1.77 Rare earth flint 1.7-1.84 Lanthanum flint 1.82-1.98 Arsenic trisulfide glass 2.04 Diamond 2.417 http://hyperphysics.phy-astr.gsu.edu/ hbase/tables/indrf.html#c1 Spectacle crown, C-1 1.523-9 -
SIMPLE LENS TYPES - 10 -
GEOMETRICAL OPTICS THIN LENS- IMAGE FORMATION Principal plane -f f 1 f = 1 s 0 + 1 s 1 s 0 object optical axis s 1 image s 0 = 5.35 cm s 1 = 14.1 cm f = 3.8 cm 1 s0 = 0.19 cm 1 1 s1 = 0.07 cm 1 1 f = 0.26 cm 1 1 cm - 11 -
GEOMETRICAL OPTICS THIN LENS- VIRTUAL IMAGE FORMATION Principal plane -f f optical axis object image - 12 -
MAGNIFYING GLASS a 2 a 1 virtual image object 250 mm f Magnifier increases the angular size of the object M=a 2 /a 1 Magnification is defined by focal distance of lens M=250/f Maximum magnification of magnifying glass is 10x-20x - 13 -
HOW DOES IT WORK? Practical realisation - 14-
COMPOUND MICROSCOPE CONVERGENT BEAM PATH Sample is placed in front of objective focal plane. Intermediate image is formed by objective and is observed through eyepiece. - 15 -
DISADVANTAGE OF A CONVERGENT BEAM PATH Convergent beam Beam is focused differently More aberrations Parallel beam Beam is only shifted Less aberration Presence of parallel light beam is microscope light path is important for modern light microscope (for filters, and other optical elements) - 16 -
COMPOUND MICROSCOPE INFINITY-CORRECTED BEAM PATH The sample is placed in the focal plane of the objective. Parallel light beams are focused by the tube lens. The intermediate image is observed through the eyepiece. - 17 -
OBJECTIVE Objective are constructed of several high quality lenses. For infinity corrected objective the specimen is in the focal plane For not infinity corrected objectives the specimen is in front of the focal plane - 18 -
EYEPIECE The eyepiece acts as a magnifier of the intermediate image - 19 -
CAMERA AS IMAGE DETECTOR When the camera is used, the intermediate image is directly projected on the camera chip (additionally an intermediate magnifier might be used). - 20 -
ANATOMY OF MICROSCOPE Two independent illumination paths: Transmission Fluorescence Components for contrasting methods: DIC Dark field Phase contrast - 21 -
HOW MICROSCOPE WORKS SUMMARY Magnifying glass has a limited magnification of 10x-20x Compound microscope makes two stage magnification initial magnification with objective further magnification with eyepiece Compound microscope beam path designs finite old microscopes infinity corrected modern microscopes There are several microscope types inverted upright - 22 -
WHAT ARE THE LIMITATIONS OF LIGHT MICROSCOPY? Physical Principles - 23-
RAYLEIGH-SOMMERFIELD DIFFRACTION Analytical solutions: Fraunhofer: small aperture, far-field Kirchhoff-Fresnel: small angle, paraxial - 24 -
LIGHT-WAVE THEORY YOUNG: DOUBLE SLIT EXPERIMENT Huygens-Fresnel Principle Each point of a wavefront can be seen as seed point for a new (circular) wave. Richard Feynman: [N]o-one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them. - 25 -
INTERFERENCE OF TWO POINT SOURCES 2 f 2 x 1 2 v 2 f 2 t x f ( x, t) a exp 2 i t k 2 2 wavenumber angular frequency phase velocity v / k f ( x, t) a exp[ i( kx t)] f ( x) a exp[ ikx)] waves in phase f ( x) cos( kx) i sin( k x) f ( y) coskrs i sin( k rs ) coskrs i sin( k rs ) 1 1 2 2 coskr i sin kr S n S n 2 2 r S y d 1 2 2 r S ( a y) d 2-26 -
INTERFERENCE CIRCULAR WAVE Wavelength: 500 nm y r = A 0 cos k r r = ( x 2 + y 2 ) k = 2π λ -4-3 -2-1 0 1 2 3 4 d / mm Superposition of circular waves k:=wavenumber 20 mm - 27 -
INTERFERENCE OF TWO POINT SOURCES 200 mm 4 I 0-20 -10 0 10 20 x / mm I = I 0 1 + kdsinθ 3 2 1 0-28 -
DIIFRACTION SINGLE SLIT 40 30 20 10 d / mm Intensity 0 I = I 0 sin( Φ 2 ) Φ 2 2-29 -
INTERFERENCE MULTIPLE POINT SOURCES /d /d /d /d 100 80 60 40 20 0-40 -30-20 -10 0 10 20 30 40 x / mm I = I 0 sin 2 N( φ 2 ) sin 2 ( φ 2 ) φ = k d sinθ - 30 -
DIFFRACTION SINGLE SLIT 400 nm 40 30 20 10 d / mm 500 nm 600 nm Intensity Intensity 0 40 30 20 10 0 40 30 20 10 d / mm d / mm 200 mm Intensity 0-31 -
DIFFRACTION SINGLE SLIT slit: 20 µm slit: 10 µm slit: 5 µm slit: 0.1 µm 500 nm Intensity Intensity Intensity Intensity 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 40 30 20 10 0 d / mm d / mm d / mm d / mm - 32 -
LIGHT-WAVE THEORY FAR FIELD DIFFRACTION Parallel light Observation plane distance R R>1.3 m Slit aperture 100 µm 40 30 20 10 d / mm Circular aperture J. Fraunhofer (1787-1826) J 1 ( Φ I = I 2 ) 0 Φ 4 2 I = I 0 Intensity 0 sin( Φ 2 ) Φ 2 2 Airy disk Φ = k a sinθ sinθ min = 1.22 λ a - 33 -
WHAT ARE THE LIMITATIONS OF LIGHT MICROSCOPY? Practical considerations - 34 -
PRACTICAL CONSIDERATIONS Illumination - 35 -
REQUIREMENTS FOR ILLUMINATION Uniform over whole field of view Has all angles accepted by objective Allows optimize image brightness/contrast Allows continuous change of intensity Allows continuous change of field of view Change in illumination and imaging parts do not effect each other Realized in Kohler illumination - 36 -
ROLE OF CONDENSER IN IMAGE FORMATION NA tot =NA obj +NA cond - 37 -
COLLECTOR AND CONDENSER Collector gathers light from light source Condenser directs light onto the specimen - 38 -
CONJUGATED PLANES IN OPTICAL MICROSCOPY Image forming light path (Observed with eyepiece) 1. Variable field diaphragm 2. Specimen plane 3. Intermediate image plane 4. Image plane (camera, retina) Illumination light path (Observed with Bertrand lens) 1. Lamp (filament, arc) 2. Condenser aperture diaphragm 3. Objective rear (back) focal plane 4. Eyepoint (exit pupil of microscope) Conjugated = imaged onto each other Has one diaphragm in every path If light at given plane is focused in one path, it is parallel in other path - 39 -
PRACTICAL CONSIDERATIONS Numerical Aperture - 40 -
DIFFRACTION ORDERS d = 2 1 st order (d = 5 ) 0-1 +1 for small enough structures a first diffraction maxima is perpendicular to the direct light d = 1 1 st order (d = 1.5 ) 0 +1 d sina m Direction of diffraction maxima depends on wavelength and period Bigger period results in smaller diffraction angle Bigger wavelength results in bigger diffraction angle - 41 -
NUMERICAL APERTURE OF OBJECTIVE NA nsina 0 a 0 n 1!! n 1.518 The NA defines how much light (brightness) and how many diffraction orders (resolution) are captured by the objective. - 42 -
ROLE OF IMMERSION NA=nsina Refractive indices: Air - 1.003 Water - 1.33 Glycerol - 1.47 Oil - 1.52 Immersion media increase the NA of an objective or a condenser by bringing the beams with higher incidence angle into the light path - 43 -
PRACTICAL CONSIDERATIONS Resolution/Contrast - 44-
DIFFRACTION LIMITED RESOLUTION d = λ 2 (n sin θ) NA = (n sin θ) Ernst Abbe 1840-1905 According to Abbe, a detail with a particular spacing in the specimen is resolved when the numerical aperture (NA) of the objective lens is large enough to capture the first-order diffraction pattern produced by the detail at the wavelength employed. In order to fulfill Abbe's requirements, the angular aperture of the objective must be large enough to admit both the zeroth and first order light waves. http://micro.magnet.fsu.edu/optics/timeline/people/abbe.html - 45 -
DEPTH OF FIELD Magnification Numerical Aperture Depth of Field (mm) Image Depth (mm) 4x 0.10 15.5 0.13 10x 0.25 8.5 0.80 20x 0.40 5.8 3.8 40x 0.65 1.0 12.8 60x 0.85 0.40 29.8 100x 0.95 0.19 80.0 d tot = λ n NA 2 + n M NA e Diffraction limited depth of field Detection system - 46 -
MODULATION/CONTRAST - 47 -
EXCURSION Fourier Transformation - 48-
SPECTRAL TECHNIQUES Fourier transform Jean Baptiste Fourier (1768-1830): (Almost) every periodic function g(x) can be described as a sum of harmonic sinusoids. Non periodic functions can also be decribed as sums of sine and cosine functions (Fourier integral; infinitely many densley spaced frequencies) Signal Processing Discrete Fourier Transform (DFT); fast algorithm Fast Fourier Transform (FFT) Discrete Cosine Transformation (DCT) - 49-
FOURIER ANALYSIS/SYNTHESIS 1.0 1.0 0.5 0.5 0.0 0.0-0.5-0.5-1.0-1.0-10 -5 0 5 10-10 -5 0 5 10 1.0 A 1.0 A 0.5 0.5 0.0 0.0-0.5-0.5-1.0-1.0-10 -5 0 5 10-10 -5 0 5 10 A A f x = a 0 2 k=1 (a k cos kπt + b k sin(k π t) - 50-
FOURIER ANALYSIS/SYNTHESIS 1.0 1.0 0.5 0.5 0.0 0.0-0.5-0.5-1.0-1.0-10 -5 0 5 10-10 -5 0 5 10 1.0 1.0 0.5 0.5 0.0 0.0-0.5-0.5-1.0-1.0-10 -5 0 5 10-10 -5 0 5 10 f x = a 0 2 k=1 (a k cos kπt + b k sin(k π t) - 51-
FREQUENCY SPECTRUM Amplitude 1.0 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 7 8 9 10 1.0 0.5 0.0-0.5-1.0-10 -5 0 5 10 f x = a 0 2 k=1 (a k cos kπt + b k sin(k π t) - 52-
FAST FOURIER TRANSFORMATION (FFT) - 53-
INVERSE FFT HIGH FREQUENCIES - 54 -
INVERSE FFT LOW FREQUENCIES - 55 -
PRACTICAL CONSIDERATIONS Aberrations - 56-
MICROSCOPE OPTICS Aberrations in optics Objective engravings Choice of magnification - 57-
OPTICAL ABERRATIONS Astigmatism (tangential and meridianal focus are different) Coma (image of dot is not symmetric) Distortion (parallel lines are not parallel in image) Curvature of the field (image of plane is not flat) Chromatic (different focus for different wavelength) Spherical (different focus for on and off axis beams) It is desired to minimize aberrations by proper use of objectives with good aberration correction - 58-
SPHERICAL ABERRATION Use cover slip 0.17 mm thick or Use objective with correction ring Avoid refraction index mismatch of immersion and mounting media - 59-
CHROMATIC ABERRATION - 60 -
OBJECTIVE TYPES Objective Type Spherical Aberration Chromatic Aberration Field Curvature Achromat 1 Color 2 Colors No Plan Achromat 1 Color 2 Colors Yes Fluorite 2-3 Colors 2-3 Colors No Plan Fluorite 3-4 Colors 2-4 Colors Yes Plan Apochromat 3-4 Colors 4-5 Colors Yes - 61-
WORKING DISTANCE AND PARFOCAL LENGTH Parfocal distance Distance from objective shoulder till specimen plane 45 mm for most manufactures, 60 mm for Nikon CFI 60 Working distance Distance from front edge of objective till cover slip Varies from several mm till several hundreds micrometers. Special long working distance objective are available. - 62 -
OBJECTIVES WITH CORRECTION COLLARS NEOFLUAR optics is less color corrected than APOCHROMAT Range of cover glass thickness W W Glyc Oil Ph = phase contrast (3 specifies matching condenser) Different immersion media under various cover glass conditions - 63 -
TOTAL MICROSCOPE MAGNIFICATION Defined by magnification of objective, eyepiece and intermediate magnification M tot =M obj x M int x M eyepiece Objective magnification defined by focal lengths of tube lens and objectives M obj =f tl /f obj Tube lens has a standardized value for specific manufacture Zeiss, Leica, Olympus 165 mm, Nikon 200 mm Typical magnification rangies: M obj : 2x 100x M int : 1.5x 2.5x M obj : 10x 25x - 64 -
USEFUL MAGNIFICATION RANGE Microscope resolution is limited by NA and wavelength. Enlargement of image does not necessarily resolve new features. Excessively large magnification is called empty magnification. (The Airy disk on retina/camera should not exceed two cell/pixel sizes). Useful magnification = 500-1000 x NA of objective M obj M eyepiece NA obj M tot M useful Magnification 10x 10x 0.35 100 175-350 low 40x 10x 0.70 400 350-700 ok 100x 10x 1.40 1000 700-1400 ok 100x 15x 1.40 1500 700-1400 empty - 65 -
MICROSCOPE OPTICS SUMMARY Correct choice of microscope optics is the key to successful imaging Pay attention to the engravings on objective and eyepiece Optical aberrations can be minimized use well corrected optics or use green filter use cover slip 0.17 mm thick match refractive index of immersion media and specimen Choose magnification carefully excessive magnification does not reveal new details moreover it deceases the brightness of the image - 66 -
CONTRASTING METHODS Dark field Phase contrast DIC PlasDIC - 67-
AMPLITUDE AND PHASE SPECIMENS Amplitude specimen changes the intensity of incident light Phase specimen changes the phase of incident light Most unstained biological specimens are phase ones - 68 -
EXAMPLES OF CONTRASTING METHODS Dark field Bone thin section Phase contrast HEK cells DIC Neurons PlasDIC HEK cells - 69 -
DARKFIELD CONTRAST 5 iris diaphragm 4 - objective 3 - sample 2 - condenser 1 - phase stop A - low NA objective B - high NA objective with iris Required: special condenser, sometimes immersion oil Principle: direct light is rejected or blocked, only scattered light is observed Disadvantage: low resolution - 70 -
INTERFERENCE Addition of waves Amplitude of the resulting wave depends on the pahse relation of two waves Extreme cases: destructive interference (res. amplitude =0) positive interference With interference a phase difference can be turned into an amplitude difference Interference is the basic principle of Phase contrast and DIC. - 71 -
PHASE CONTRAST MICROSCOPY - 72 -
PHASE CONTRAST MICROSCOPY 9 - intermediate image 8 - tube lense 7 - indirect light 6 - direct light 5 - phase ring 4 - objective 3 - sample 2 - condenser 1 - phase stop Required: special objectives and special condensers. Principle: direct light is attenuated and its phase is shifted 90. Contrast formed due to interference between direct and scattered light. Disadvantages: relatively low resolution, halos - 73 -
DIFFERENTIAL INTERFERENCE CONTRAST 9 - intermediate image 8 - tube lens 7 analyzer 7a - λ-plate 6 - Wollaston prism 5 objective 4 sample 3 condenser 2 Wollaston prism 1 - polariser Required: special accessories in light path (prisms, polarizers). Principle: specimen is sensed with two linear polarized slightly shifted (< ) light beams. Difference in optical path of the beams gives a contrast in image. Disadvantages: accessories are relatively expensive. - 74 -
DIC IN DETAILS DIC prism split beam into two perpendicularly polarized. Shift between beams less that resolution of microscope. Beams measure difference in optical path in specimen. If retardation is not zero, they are interfere after being recombined on the second DIC prism. - 75 -
PLASDIC Required: slit diaphragm, prism with polarizer, analyzer. Principle: A slit diaphragm creates a pair of non-polarized light beams that are /4 out-of-phase. The beams get polarized just before being recombined into a single beam in the DIC-prism. The analyzer (linear) sets a single polarization plane where the components of the beam can interfere. - 76 -
CONTRASTING TECHNIQUES SUMMARY Dark field Fine structural features at, and even below, the resolution limit of a light microscope. Highly suitable for metallographic and crystallographic examinations with reflected light. Phase contrast Used for visualizing very fine structural features in tissues and single cells contained in very thin (< 5 µm), non-stained specimens. DIC Method shows optical path differences in the specimen in a relieflike fashion. The method is excellently suited for thick, non-stained specimens (> 5 µm). Can be used for optical sectioning. PlasDIC The same specimen as conventional DIC but in plastic dishes. - 77 -
IMAGES ARE ARTEFACTS Two images of same object (sample) imaged with the same microscope/objective! Object Image of Object - 78 -
MORE ABOUT LIGHT MICROSCOPY 1. Lecture Biomicroscopy I + II, Prof. Theo Lasser, EPFL 2. Books a) Digital microscopy, Sluder, G; Wolf, D.E., eds, Elsevier, 2003 b) Optics, 4th ed., Eugene Hecht, Addison-Wesley, 2002 3. Internet a) http://micro.magnet.fsu.edu b) b) Web sites of microscope manufactures Leica Nikon Olympus Zeiss 4. BIOp EPFL, SV-AI 0241, Sv-AI 0140 http://biop.epfl.ch/ - 79 -
Acknowledgments These slides are based on a lecture given by Yuri Belyaev (Advanced Light Microscopy Facility, EMBL Heidelberg) during a practical course concerning basics of light microscopy. Thus a big thank to him for providing them and making them available also here at EPFL. - 80 -