A. La Rosa Lecture Notes Portland State University

APPLIED OPTICS ________________________________________________________________________ DESIGN of OPTICAL INSTRUMENTS: The Koehler Illumination.

Harnessing illumination-control in optical systems.

References: Basic Concepts in Optical Microscopy https://www.olympus-lifescience.com/en/microscope-

resource/primer/anatomy/anatomy/ How to Set Up Koehler Illumination (video) https://www.ibiology.org/talks/set-up-koehler-

illumination/ I. Introduction II. The conventional microscope III. Description of the Koehler Illumination III.1 Filament and lamp collector III.2 The condenser lens III.3 Independent control of the dimension and light intensity of the illuminated field

area III.3.A The role of the Field Diaphragm III.3.B The role of the Aperture Diaphragm III.4 Complete optical setup

Fila- ment

Retina

Field diaphragm

Each point of the light source produces a uniform illumination on the specimen plane. The field diagram is uniformed illuminated. Since each point of the field diagram is imaged on the specimen plane, then a uniform illumination is obtained at the specimen.

I. Introduction We describe an illumination method, introduced by August Koehler in 1893, that allows attaining a uniform illumination on a sample within an optical microscope, despite the eventual use of non-homogeneous sources (like electrical lamps).

As described in more detail below, the Koehler illumination setup presents two main characteristics:

• Creates an evenly illuminated field of view • The light intensity at specimen plane and the size of the illuminated field can be

regulated independently

These features are attained by placing two distinct sets of optical elements across the microscope:

• a set of “illumination apertures” A1, A2, A3, A4, and

• a set of “illuminated field diaphragms” F1, F2, F3, F4.

These two sets are schematically shown in Fig.1a and Fig.1b below, but a more detailed explanation follows in the next sections.

f1 f1

Lamp collector

Fila- ment

Filament’s image

Condenser lens

fcond fcond

Objective lens

fobj fobj

Eyepiece lens

fe fe

A1 A2 A3 A4

WD

Object’s image on the user’s

retina

Object

Fig. 1 Illumination apertures-diaphragms A1, A2, A3, A4. (The complementary field-diaphragms that limit the width of the cone of rays in the system are not shown). The figure shows how a particular cone of light emitted from a point on the filament is spread out uniformly across the specimen’s plane (a more detailed justification of the ray tracing is given in the main text). In addition, it will be shown that the diaphragm A2 controls the light intensity reaching the sample without modifying the size of the illuminated area on the specimen’s plane.

fcond f1 f1

Lamp collector

Fila-ment

Filament’s image

Condenser lens

fcon

Objective lens

fobj fobj

Eyepiece lens

fe fe

F1 F2 F3 F4

Oject’s image on the user’s

retina

Object

WD

Fig. 2 Field diaphragms F1, F2, F3, F4. (The complementary illumination apertures that control the intensity reaching the specimen are not shown). Notice in this set up that i) each point on the field-diaphragm behaves as a point source of light, and ii) the diameter of the field-diaphragm F1 is imaged at the specimen’s plane. Accordingly, the size of the region illuminated at the specimen’s plane is controlled by the field-diaphragm F1.

II. The conventional microscope

The Koehler illumination is to improve the quality of a conventional optical microscope where:

an objective-lens forms a first image at the front focal plane of the eyepiece, and the latter forms a virtual image at infinity. This implies that a bundle of parallel rays reaches the user’s eye, and a real final image is formed at the user’s eye retina.

If the illumination on the object is not uniform, the corresponding image will display such low quality light distribution.

It is in this optical microscope setup that we are going to introduce a proper illumination, the Koehler illumination, to a) fully exploit the maximum resolution of the microscope objective (by being able to select the proper numerical aperture of the condenser lens as to match that of the objective lens), b) obtain an uniform illumination over the sample despite using lamps of non-uniform brightness, while c) minimizing vigneting (the filament is imaged at the user’s eye lens.)

Objective lens

fobj fobj

Eyepiece lens

fe fe

Exit pupil

First mage’s plane (front focal plane of the eyepiece)

Object’s image on the user’s retina

Aperture

stop

Object Optical tube length

Illumi-nation WD

fhuman eye

Fig. 3 Basic components of an optical microscope. An object is placed at a proper working distance (WD) from the objective-lens. The diagram correspond to an old fashion microscope where a tube length specifies where the first image is formed. (Nowadays, infinitely corrected objective lenses are used instead).

Objective lens

fobj fobj

Eyepiece lens

fe fe

Exit pupil

First mage’s plane (front focal plane of the eyepiece)

Object’s image on the user’s retina

Object Optical tube length

Illumi-nation WD

fhuman eye

Aperture stop

Fig. 4 Basic components of an optical microscope.

III. Description of the Koehler Illumination We show the ray tracing starting from the illumination section towards the sample

stage, and then to the ocular eyepiece. In the final part we outline some hands on “tricks” on how to actually implement the Koehler illumination (we’ll see that the order of descriptions reverses, starting rather from the sample stage and continues with the illuminating lamp set up.)

III.1 Filament and lamp collector • The purpose is to place the image of the filament at the back focal plane of the

condenser lens • Notice the magnification of the filament’s image changes with the filament’s

position. In practice, since the illumination set-up (i.e. filament’s position) is rarely changed, the lamp position is chosen at the very beginning of the setup such that the filament’s image fills the largest diameter of the aperture diaphragm A2. (As a consequence, when working with the aperture diaphragm A2 at lower openings, the lamp’s light power will be used less efficiently.)

f1 f1

Lamp collector

Filament’s image

Condenser lens

fcond fcond

Obj l

fobj

F2

A1 A2 F1

Field diaphragm (back focal plane of lamp

collector lens)

G R P

Aperture diaphragm (or sub stage diaphragm) (Located at the front focal

plane of the condenser lens)

Filament

Position of the filament selected such that its image fills the max aperture of A2.

f1 f1

Lamp collector

Filament’s image

Condenser lens

fcond fcond

O ba

Objecti lens

fobj fo

F2

A1 A2 F1

Field diaphragm (Placed at the back focal plane of lamp

collector lens)

G R P

Aperture diaphragm (or sub stage diaphragm) (Located at the front focal

plane of the condenser lens)

Filament

Fig. 5 Filament placed in such a way that its image fills the max aperture of A2. Such a filament image is located at the front focal plane of the condenser lens.

• Notice that the field diaphragm F1 (located at the back focal plane of the lamp collector) is uniformly illuminated

Indeed, notice in Fig. 5 above that it doesn’t matter whether or not the point sources G, R, and P at the filament are of equal intensity. If, for example, one of those sources were off, the overall illumination would certainly be dimmer, but the intensity across the field diaphragm would still be uniform. (The latter gives us an extra clue: To image the field diagram plane F1 onto the object-plane. That way we will obtain a uniform illumination on the object plane, regardless of the inhomogeneous structure of the filament.)

III.2 The condenser lens

• One of the roles of the condenser lens is to image the field diaphragm (F1) into the object’s plane F2.

Objec back-f

plan

Obj l

fobj fobj

A3

G R P

Filament

Filament’s image

Object

Lamp collector

Condenser lens

Field diaphragm (back focal plane of lamp

collector lens)

f1 f1 fcond fcond

A1 A2 F1

Aperture diaphragm (or sub stage diaphragm)

(Located at the front focal plane of the condenser lens)

F2

Object’s plane

Fig. 6 Field diaphragm F1 imaged at the object’s plane F2.

• The aperture diaphragm A2 controls the numerical aperture of the

condenser lens

Notice in the figure below that the smaller aperture A2 the smaller the angle θ. This is an important feature, since, ideally, the numerical aperture of the condenser lens should match the numerical aperture of the objective-lens. For a given objective lens, the Koehler illumination allows using the aperture diaphragm A2 to match that value.

Objec back-f

plan

Obj l

fobj fobj

A3

Filament’s image

Object

θ

Lamp collector

Condenser lens

Field diaphragm (back focal plane of lamp

collector lens)

f1 f1

F1

G R P

Filament

fcond

A1 A2 F2

fcond

Fig. 7 The size of the aperture diaphragm A2 determines the condenser’s numerical aperture.

III.3 Independent control of the dimension and light intensity of the illuminated field area (equivalently, independent control of the illuminated field area and the condenser’s numerical aperture)

III.3.A The role of the Field Diaphragm F1 • The field diaphragm (F1) controls the size of the illuminated area

on the object’s plane (F2). Visual justification of the statement: Pay attention in Fig. 8 how F1 controls the size of the bundle of rays emitted from each particular point of the filament. Notice, if we decreased the size of the field diagram (F1) then each particular bundle of parallel rays reaching the specimen would become thinner, thus illuminating a smaller area of the specimen. A more analytical justification: By design, “the object’s plane F2 is the image of the field diaphragm (F1)”. Hence, we have then a linear-magnification relationship between the size of the aperture F1 and the size of the illuminated area in the object’s plane. The larger field diaphragm (F1) the larger size of the illuminated area on the object’s plane (F2)

• A decrease in the field diaphragm (F1) does not affect the light intensity (or power density Watt/m2) received at the object’s plane.

The reason is that a uniform distribution of light (across the diameter of the aperture) passes through F1 (as seen in Fig. 8). That uniformity will be observed also at the objects’ plane (where the rays in the bundles arrive in parallel). Hence, decreasing the size of diaphragm F1 is translated in a decrease of the illuminated area on the objects’ plane, without changing the uniformity of the illumination.

f1 f1

Lamp collector

Condenser lens

fcond fcond

Objective back-foca

plane

fobj fobj

A3

A1 A2 F1

Field diaphragm (back focal plane of lamp

collector lens)

G R P

A uniform distribution of light passes across

this aperture

Filament

A uniform distribution of light reaches the

objects plane

F2

Object

Fig. 8 By changing the size of the field diaphragm F1 one controls the size of the illuminated area on the object’s plane, but the power density (Watt/m2) of the illuminated area remains constant. In passing, notice also, that each point of the filament produces a uniform illumination on the object plane.

F1

F1

Object

Object

Fig. 8 (complement analogy.) “A decrease in the field diaphragm (F1) does not

affect the light intensity (or power density Watt/m2) received at the object’s plane.” It is similar to the case in which a light beam passes through a window; if we decrease the size of the window certainly less light passes through, but the intensity (energy per unit area) remain the same. The size of the beam reaching the object decreases, but the intensity remains the same.

Question: Would “P” and ”R” produce illuminated areas of the same size on the plane F2?

Answer: Yes, because the diameter of the field-diaphragm F1 is imaged at the specimen’s plane (as seen in Fig.7).

Question: In Fig. 8 why do each bundle arriving to the object plane appear to

have the same size? Answer: Because the diameter of the field-diaphragm F1 is imaged at the

specimen’s plane (as seen in Fig.7).

III.3.B The role of the Aperture Diaphragm A2 • The aperture diaphragm (A2) controls the light intensity reaching the object, but

without affecting the size of the illuminated area. Justification of the statement: First, notice in Fig 9 that each point on the aperture A2 generates a bundle that illuminates uniformly the same region on the object-plane.

The reason again is that “the object’s plane F2 is the image of the field diaphragm (F1)” The image size depends on the condenser lens; an opening (like the aperture A2) is not going to affect the size of the image. (The size of the illuminating parallel-rays bundle is controlled by F1, not by A2.)

Accordingly, if we decreased the size of the aperture diagram (A2) then we are decreasing is the number of bundles arriving at the object’s plane (hence decreasing the light intensity) but not the size of the illuminated area.

f1 f1

Lamp collector

Condenser lens

fcond fcond

Objective back-focal

plane

fobj fobj

(front

the

A1 A2 F1

Field diaphragm (back focal plane of lamp

collector lens)

G R P

Each point on the aperture A2 generated

a bundle.

Filament

All the different bundles illuminate the same area. The number of bundles is

controlled by the A2 aperture.

F2

Object

Fig. 9 The aperture diaphragm A2 controls the number of bundles arriving to the objects plane (hence controlling the illumination intensity) but not the size of the bundles (hence without modifying the area illuminated on the objects plane.)

In short, the aperture diaphragm (A2) and the field diaphragm (F1) affect independently the optical setup.

III.4 Complete optical setup The above description constitutes the expected arrangement in a Koehler illumination setup. The resulting full ray tracing in the optical microscope is shown below.

A1

f1 f1

Field diaphragm

(Back focal plane of lamp collector lens)

Filament

Filament’s image

Condenser lens

Object plane

fcond fcond

Objective back-focal

plane

Objective lens

fobj fobj

Eyepiece lens

fe fe

Exit pupil

First-image’s plane (front focal plane of the eyepiece)

A2 A4

A4

Image on the user’s retina

A3 F1 F2 F3

Lamp Collector

lens

F4

WD

(Front focal plane of the condenser

lens)

AS EnP

Fig. 10 Notice how each point source (cone of light) from the filament i) arrive uniformly spread over the specimen object’s plane, and ii) if the diameter of the aperture diaphragm were to be reduced, then less number of point sources from the filament will arrive to the specimen’s plane, however each cone that goes through will illuminate the same specimen’s region. Hence, the diaphragm control the intensity of light reaching the specimen but without altering the size of the illuminated area on the specimen’s plane.

Additional information (in preparation) 1.

Ref https://www.olympus-lifescience.com/en/microscope-resource/primer/anatomy/introduction/ 2.

Microscope illumination system Ref: https://www.olympus-lifescience.com/en/microscope-resource/primer/anatomy/kohler/

3.

Ref https://www.zeiss.com/microscopy/us/solutions/reference/basic-microscopy/koehler-illumination.html

4.

Ref https://www.olympus-lifescience.com/en/microscope-resource/primer/anatomy/kohler/

5. Steps in Establishing Köhler Illumination Ref:https://www.zeiss.com/microscopy/us/solutions/reference/basic-microscopy/koehler-illumination.html 6. Starting with the objective lens and the eyepiece in their proper position,

• image the field diaphragm F1 in the object’s plane For that purpose, have the field diaphragm quite open and try to obtain a sharp image of the borders. You achieve that placing the condenser lens in the proper position.

• Image the filament in the front focal plane of the condenser lens. You can obtain this by placing a piece of upper in the back focal plane of the objective lens. A clear image of the filament should be obtained there.

7.

8.

Ref: http://snyder.ucalgary.ca/imaging/system/files/2011All+Widefield+Protocols.pdf

http://snyder.ucalgary.ca/imaging/system/files/2011All+Widefield+Protocols.pdf --------------------------------------------------------------------------------------------------------------------------------------------

Setting up Köhler illumination http://www.quekett.org/resources/kohler

V. REFERENCES C. Hammond, "Symmetrical Ray Diagrams of the Optical Pathways in Light Microscopes" The Americas Microscopy and Analysis, Sept Issue, p. 5-8 (2006). The article considers infinity corrected optics C. Hammond, “A symmetrical representation of the geometrical optics of the light microscope,” Journal of Microscopy. 192, 63–68 (1998). Shinya Inoue, K. R. Spring, “Video Microscopy, the Fundamentals” 2nd Ed. Plenum Press (1997).

Backup figure

A1

f1 f1

Field diaphragm

(back focal plane of lamp collector lens)

Lamp collector

Filament

Filament’s image

Condenser lens

Aperture diaphragm (or substage diaphragm) (In the front focal plane of the

condenser lens)

Object

fcond fcond

Objective back-focal

plane

Objective lens

fobj fobj

Eyepiece

fe fe

Exit pupil

First mage plane (front focal plane of

the eyepiece)

A2 A3 A4 F1 F2 F3 F4

Image on the user’s retina

Backup figure

A1

f1 f1

Field diaphragm

(back focal plane of lamp collector lens)

Lamp collector

Filament

Filament’s image

Condenser lens

Aperture diaphragm (or substage diaphragm) (In the front focal plane of the

condenser lens)

Object

fcond fcond

Objective back-focal

plane

Objective lens

fobj fobj

Eyepiece

fe fe

Exit pupil

First mage plane (front focal plane of

the eyepiece)

A2 A3 A4 F1 F2 F3 F4

Image on the user’s retina