16. Proposal for a Phase Contrast X-ray Microscope

G. Schmahl and D. Rudolph

F orschungsgruppe Rontgenrnikroskopie, U niversitat Gottingen, Geismarlandstr. 11 ,

D-3400, Gottingen, Fed. Rep. of Germany

Introduction

In x-ray microscopy experiments performed up to now the con­

trast is dominated by photoelectric absorption. The resulting radiation

dose, though much less than in electron microscopy, limits fundamen­

tally the resolution which can be obtained when investigating biolog­

ical materials in the natural (intact wet and unstained) or living state,

Sayre et al. (1977). Investigations to decouple resolution and radiation

dose leads to a proposal for a phase contrast x-ray microscope. This

work is based on experimental results on phase zone plates,

Hilkenbach and Thieme (1986), and on the atomic scattering factors

published by Henke (1981).

Phase Contrast X-ray Microscope

In Figure 16.1 the x-ray optical set up of an x-ray phase contrast

microscope is shown. The object is coherently illuminated. A thin plate

called the phase plate is placed in the back focal plane of the micro

zone plate. This phase plate retards or advances the phase of the cen­

tral order with respect to the diffraction spectra by one-quarter of a

period.

We consider an object with the thickness t, consisting of different

components with the refractive indices nj according to Figure 16.2.

With n = 1 - 8 - i {3, the amplitude transmission is given by

X-ray Microscopy Ed. by P. c. Cheng and G. J . Jan © Springer-Verlag Berlin Heidelberg 1987

232

(16.1)

If we consider a pure phase object and are only interested in the dif­

ferences of the phase shift caused by the different components, we can

write

With

we can write

X- radiation from condenser

object

X,Y

~(xtY) = ei 2; 8(xJ1)t

back focal plane

zone plate

V I

I I I

phase plate

Figure 16.1. Schematic of a phase contrast x-ray microscope

(16.2)

(16.3)

(16.4)

image plane

X', Y'

233

" " " t ++++++ " " " " " ++++++ " " " " " " " " " ++++++ " " " " ++++++ " " " " " t " " " " ++++++ " " " " " ++++++ " " " " ++++++ " " " " " ~ " " " " " " " " " " " " "

"1 "2 "3

Figure 16.2. Object consisting of different components with refractive indices

The phase plate in Figure 16.1 will cause a light distribution in the

image plane which represents a fictitious amplitude object

II

T(xJ') = ± i + icf>(xJ') (16.5)

The intensity in the image plane is therefore proportional to

II 2 I(x J' ) = I T(xJ') I = 1 ± 2cf>(xJ') (16.6)

with x' = V x, y'= V y, V = x-ray magnification. In this case, it is

assumed that the transmission of the phase plate is 100%.

We consider now two different object structures, both of thick­

ness t, and the resulting intensities

and

(16.7)

In the following we restrict to the upper sign in (16.7) which described

the case where t~e phase of the central order is retarded with respect

to the diffraction spectra.

234

I} - 12 • • The contrast in the image plane K = IS gIven by

I} + 12

4>1 (XJI) - 4>2(XJI) Kp = ---------

1 + 4>1 (XJI) + 4>2(XJI) (16.8)

If we observe the same structures without the phase plate, i.e. in am­

plitude contrast caused by photoelectric absorption, only the first fac­

tor in eq. (16.1) counts resulting in the transmission function

(16.9)

With the linear absorption coefficient ILl = :'" f3 and weak absorption,

i.e. ILl < < 1, one obtains

(16.10)

Considering again two different object structures the resulting inten­

sities in the image plane are proportional to

II (x,y) = 1 - ILl, 1 (XJI)t

h(x,y) = 1 - ILI2(XJI)t ,

The contrast KA is, therefore, given by

(ILI,2(XJI) - ILl, 1 (XJI))t KA = ----------

2 - (ILl, 1 (XJI) + ILI,2(XJI))t

(16.11)

(16.12)

It should be mentioned that the illumination of the object, shown as

coherent illumination in Figure 16.1, in practical cases will be partial

coherent.

235

Phase Contrast Versus Amplitude Contrast - Numerical Examples

To calculate the phase and amplitude contrast according to (16.8)

and (16.12) the 8- and f3- values have to be derived using the relations

2 2 '0'11. - '0'11. -

(16.13) 8 = --nil f3 = 2:;;:- nl2 2'1T

with

11 = Ln.J'l,k 12 = L n.J'2,k (16.14) k k

nk is the percentage number of atoms of type k in the compound, n is

given by

n= 23

6.022 x 10 Np[cm-3] M

(16.15)

with M = molecular weight, i.e. the weight in gram of one mol of the

compound, N = number of atoms of the compound, p = density in , gram cm-3 '0 is the classical electron radius, _0_ = 4.485xl0- 14cm.

2'1T The atomic scattering factors it k! h k are listed in tables published by

Henke et. al. (1977). A compound differs from a molecule by a con­

stant factor for all atoms in the molecule. For example we consider a

protein with p = 1.35gcm-3 with the relative mass fractions mH =

0.065, me = 0.530, mN = 0.160, ma = 0.230, ms= 0.015 correspond­

ing to a composition of the compound (empirical formula)

C94H 13gN24 0 3 IS. In this case it is M = 2132.4 g mol-I, N = 289, n = 1.10 x 1023 and e.g. nH = 0.48.

In the following we consider a cube of protein with 50nm length

with the above mentioned composition surrounded by water. Table

16.1 shows the phase contrast Kp and amplitude contrast KA for the

three wavelengths A = 0.62nm, A = 2.48nm and A = 4.5nm.

236

A [nm] Kp KA

0.62 1% 0.003%

2.48 4.9% 3.5%

4.50 2.8% 0.02%

Table 16.1. Phase contrast K'p and amplitude contrast KA for a 50nrn protein struc­

ture surrounded by water

The table shows that phase contrast is larger than the amplitude

contrast. More detailed investigations show that this is true for the

whole wavelength range interesting for soft x-ray microscopy and for

other organic material in wet and dry state.

One conclusion is that the wavelength region suited for high re­

solution x-ray microscopy can be extended to shorter wavelengths as

considered up to now. In another paper of this volume an x-ray image

of a part of a human fibroblast, critical point dried, is shown, Meyer­

Ilse et al. (1986). The picture has been made with A = 4.5nm, showing

a part of the nucleus in amplitude contrast. Calculations show, that

50nm dry protein structures have an amplitude contrast of 1.4 %

which corresponds closely to the value shown in Table 16.1 for protein

in water for the wavelength A = 0.62nm in phase contrast.

The phase contrast values of Table 16.1 have been calculated un­

der the assumption that the phase plate has an amplitude transmission

of 1. In practice, all phase plates for soft x-radiation have an amplitude

transmission of less than one. This leads to a better adaption of the

intensities of the central order and the diffraction spectra and, there­

fore, to an enhanced phase contrast. The phase contrast in this c~se is

in good approximation given by eq. (16.8), divided by the amplitude

transmission A of the phase plate. Table 16.2 shows thickness, trans­

mission and phase contrast enhancement for different materials and

wavelengths.

237

t[nm] T l / A

;\[nm] Cr Ni Au Re Cr Ni Au Re Cr Ni Au Re

0.62 450 350 328 400 67 % 54% 46 % 2.6 % 1.2 1.4 1.5 6.2

2.48 230 133 123 100 57 % 51 % 5.3 % 9 % 1.3 1.4 4.4 3.3

4.50 105 77 149 91 45 % 29 % 1.3 % 2.8 % 1.5 1.9 8.8 6.0

Table 16.2 . Thickness, transmission and phase contrast enhancement for different

materials and wavelength. t[nm] : thickness of the phase plate, T:

transmission of the phase plate, 1/ A: phase contrast enhancement

There are several advantages in using shorter wavelengths than

used up to now:

1. The radiation dosage applied to the object is considerably reduced.

2. Thicker specimens than up to now can be investigated.

3. The numerical apertures of zone plates are smaller resulting in

larger depths of focus and larger object distances.

4. The absorption in air and helium is much smaller.

5. The absorption of the supporting foils of zone plates, filters and

specimen holders is rather low.

6. The detective quantum efficiency (DQE) of CCD cameras is

higher.

Disadvantageous is that zone plates have to be built with higher

aspect ratios and that the total length of the x-ray microscope will be

increased.

We hope that the phase contrast method in x-ray microscopy will

play an important role for future biological and medical investigations

as it is the case in light and electron microscopy.

238

Acknowledgement

This proposal has been reported at the ESRF - EMBL Workshop on X-ray

Microscopy, Heidelberg, December 12,1986.

X-ray Microscopy Instrumentation and Biological Applications

Edited by

Ping-chin Cheng and Gwo-jen Jan

With 180 Figures and 16 Plates

Springer-Verlag Berlin Heidelberg New York London Paris Tokyo

Professor Dr. fuG-CHIN CHE."G Depanment of Electrical and Computer Engineering State University of New York at Buffalo Buffalo , NY 14260, USA

Professor Dr. GWO-JEN JAN Department of Electrical Engineering School of Engineering

ational Taiwan University Taipei Taiwan , 10764, Republic of China

ISBN 3-540-18148-2 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-18148-2 Springer-Verlag New York Berlin Heidelberg

Library of Congress Cataloging· in· Publication Data. X-ray microscopy: instrumentation and biological applications: proceedings of the X·ray microscopy 86, Taipei, Taiwan, Republic of China, August 13-15, 1986 1 edited by Ping-chin Cheng and Gwo· jen Jan. Bibliography: p. Includes index. ISBN 0-387-18148-2 (U.S.). 1. X-ray microscopy-Congres­ses. 1. Cheng, Ping-chin 1952-. II. Jan, Gwo-jen , 1946-. [DNLM: 1. Microscopy-methods-congres­ses. 2. Radiation , Ionizing-congresses. QH 212.X2 X12 1986]. QH 212.x2X23. 1987. 87-28443.

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