Imaging biological specimens with high-intensity soft x rays

Johndale C. Solem

doi:10.1364/JOSAB.3.001551

Journal of the Optical Society of America B
Vol. 3,
Issue 11,
pp. 1551-1565
(1986)
•https://doi.org/10.1364/JOSAB.3.001551

Imaging biological specimens with high-intensity soft x rays

Johndale C. Solem

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Johndale C. Solem, "Imaging biological specimens with high-intensity soft x rays," J. Opt. Soc. Am. B 3, 1551-1565 (1986)

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Abstract

I compare alternative techniques for x-ray imaging of biological specimens on the basis of (1) transverse and longitudinal resolution, (2) depth of field, (3) choice of recording medium, and (4) recording efficiency. I show that, for all imaging techniques, the dosages suffered by specimens are so high that the living state cannot be preserved, nor can the structural integrity of the specimen be maintained in the usual sense. I demonstrate the remarkable fact that, at sufficiently high intensity, an image of diffraction-limited resolution can be captured before the specimen is obliterated.

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Specimen	Mass (g)	Least Dimension (nm)	Greatest Dimension (nm)	Dosage (rad) Assuming ∊ = 1 and hv = 400 eV
				Value of δ, Contact or Lens Imaging				Value of δ, Microholography
				5 nm	10 nm	20 nm	50 nm	5 nm	10 nm	20 nm	50 nm
Tobacco necrosis viron	10⁻¹⁸	7 × 10⁰	2 × 10¹	1 × 10¹⁴	–	–	–	1 × 10¹⁴	–	–	–
Escherichia coli phage ϕx 174	10⁻¹⁷	2 × 10¹	2 × 10¹	1 × 10¹⁴	2 × 10¹²	–	–	1 × 10¹⁴	2 × 10¹²	–	–
Herpes viron	10⁻¹⁶	8 × 10¹	8 × 10¹	1 × 10¹⁴	2 × 10¹²	3 × 10¹⁰	–	1 × 10¹⁴	2 × 10¹²	3 × 10¹⁰	–
Vaccinia viron	10⁻¹⁵	2 × 10²	2 × 10²	4 × 10¹⁵	6 × 10¹³	9 × 10¹¹	4× 10⁹	4 × 10¹⁵	6 × 10¹³	1 × 10¹²	1 × 10¹⁰
Mycoplasma pneumoniae	10⁻¹⁴	3 × 10²	3 × 10²	2 × 10¹¹	3 × 10⁹	5 × 10⁷	3 × 10⁵	2 × 10¹¹	3 × 10⁹	6 × 10⁷	6 × 10⁵
Escherichia coli (immature)	10⁻¹³	4 × 10²	1 × 10³	2 × 10¹¹	3 × 10⁹	5 × 10⁷	3 × 10⁵	2 × 10¹¹	3 × 10⁹	6 × 10⁷	6 × 10⁵
Escherichia coli (mature)	10⁻¹²	8 × 10²	2 × 10³	2 × 10¹¹	3 × 10⁹	5 × 10⁷	3 × 10⁵	2 × 10¹¹	3 × 10⁹	6 × 10⁷	6 × 10⁵
Anthrax bacterium	10⁻¹¹	2 × 10³	6 × 10³	2 × 10¹¹	3 × 10⁹	5 × 10⁷	3 × 10⁵	2 × 10¹¹	4 × 10⁹	7 × 10⁷	7 × 10⁵
Red blood cell (human)	10⁻¹⁰	2 × 10³	8 × 10³	3 × 10¹¹	4 × 10⁹	7 × 10⁷	4 × 10⁵	3 × 10¹¹	5 × 10⁹	9 × 10⁷	9 × 10⁵
White blood cell (human)	10⁻⁹	5 × 10³	1 × 10⁴	2 × 10¹¹	3 × 10⁹	5 × 10⁷	3 × 10⁵	3 × 10¹¹	4 × 10⁹	8 × 10⁷	8 × 10⁵
Amoeba (dysentery)	10⁻⁸	2 × 10³	2 × 10⁴	1 × 10¹¹	2 × 10⁹	3 × 10⁷	2 × 10⁵	1 × 10¹¹	2 × 10⁹	4 × 10⁷	4 × 10⁵
Smooth muscle cell	10⁻⁷	1 × 10⁴	5 × 10⁵	2 × 10¹²	3 × 10¹⁰	8 × 10⁸	3 × 10⁶	3 × 10¹²	4 × 10¹⁰	8 × 10⁸	8 × 10⁶
Paramecium (protozoan)	10⁻⁶	6 × 10⁴	3 × 10⁵	7 × 10¹⁹	1 × 10¹⁸	2 × 10¹⁶	1 × 10¹⁴	9 × 10¹⁹	2 × 10¹⁸	3 × 10¹⁶	3 × 10¹⁴

Type	Contact Imaging		Lens Imaging		Microholography
Type	Contact Imaging		Optical Microscope	Scanning Illuminator	Fresnel Transform	Fourier Transform
Transverse resolution (δ)	max (λ, Δ)		max (λ, Δ, S)		max(λ, 2Δ)	max(λ, 2S)
Longitudinal resolution	δ²/λ
Depth of field	δ²/λ				Generally ≫ δ²/λ
Recording medium/detector	Single-layer resist	Multilayer resist with	Film	Proportional counter	Single-layer resist with variable-angle readout	Film Resist Wire chamber Photocathode
Recording efficiency (∊)	< μ_rδ²/λ	~1	½[1 − (λ/S)²}^1/2] or better with condensor lens	~1	~1

(I) Illustration R₀ = Globule radius δ = Resolution
(II) Exposure time	${[\frac{c δ^{2}}{F (γ, η) (c - 1) s I}]}^{1 / 3}$	High Contrast	Low Contrast
(II) Exposure time	${[\frac{c δ^{2}}{F (γ, η) (c - 1) s I}]}^{1 / 3}$	$\frac{δ}{2 R} {[\frac{δ^{2}}{4 G (γ, η) s I}]}^{1 / 3}$	${[\frac{c {(c^{1 / 3} - 1)}^{2} {R_{0}}^{2}}{F (γ, η) (c - 1) s I}]}^{1 / 3}$
(III) Intensity required for contact/lens imaging	$\frac{1}{s} {[{(\frac{6 N h ν}{π ρ_{0} ∊})}^{3} \frac{F (γ, η) (c - 1)}{c δ^{11}}]}^{1 / 2}$	$\frac{1}{s} {[{(\frac{3 N h ν}{{π R}_{0}^{2} ρ_{0} ∊})}^{3} \frac{G (γ, η)}{2 δ^{5}}]}^{1 / 2}$	$\frac{1}{(c^{1 / 3} - 1) s} {[{(\frac{3 N h ν}{4 π ρ_{0} ∊})}^{3} \frac{F (γ, η) (c - 1)}{{c R}_{0}^{11}}]}^{1 / 2}$
(IV) Intensity required for microholography	${[{(\frac{9 N h ν}{{π ρ}_{0}^{2} ∊})}^{3} \frac{F (γ, η) (c - 1)}{c s^{5} δ^{14}}]}^{1 / 2}$	${[{(\frac{9 N h ν}{{16 π ∊ ρ}_{0}^{2} ξ})}^{3} \frac{G (γ, η)}{s^{5} {R_{0}}^{15}}]}^{1 / 2}$	$\frac{27}{64 (c^{1 / 3} - 1)} {[{(\frac{N h ν}{{π ρ}_{0}^{2} ∊})}^{3} \frac{F (γ, η) (c - 1)}{{R_{0}}^{14} s^{5} c}]}^{1 / 2}$
$ξ = \frac{κ^{5 / 3} + 5 κ^{- 1 / 3}}{{R_{0}}^{1 / 3}} - 5 {(2 / δ)}^{1 / 3}$

(1) Specimen
Resolution (nm)	10	10	10	10
Globule radius (nm)	50	50	2.5	2.5
Contrast ratio (c)	∞	5	∞	5
(II) Contact/Lens
Intensity (w cm⁻²)	1.0 × 10¹⁰	8.9 × 10⁹	7.1 × 10¹¹	1.1 × 10¹²
Exposure time (nsec)	3.0 × 10⁻²	3.4 × 10⁻²	3.4 × 10⁻³	2.2 × 10⁻³
(III) Microholography
Intensity (w cm⁻²)	1.8 × 10¹³	1.6 × 10¹³	5.9 × 10¹⁵	5.9 × 10¹⁵
Exposure time (ns)	2.5 × 10⁻³	2.8 × 10⁻³	1.7 × 10⁻⁴	1.2 × 10⁻⁴

Specimen	Mass (g)	Least Dimension (nm)	Greatest Dimension (nm)	Dosage (rad) Assuming ∊ = 1 and hv = 400 eV
				Value of δ, Contact or Lens Imaging				Value of δ, Microholography
				5 nm	10 nm	20 nm	50 nm	5 nm	10 nm	20 nm	50 nm
Tobacco necrosis viron	10⁻¹⁸	7 × 10⁰	2 × 10¹	1 × 10¹⁴	–	–	–	1 × 10¹⁴	–	–	–
Escherichia coli phage ϕx 174	10⁻¹⁷	2 × 10¹	2 × 10¹	1 × 10¹⁴	2 × 10¹²	–	–	1 × 10¹⁴	2 × 10¹²	–	–
Herpes viron	10⁻¹⁶	8 × 10¹	8 × 10¹	1 × 10¹⁴	2 × 10¹²	3 × 10¹⁰	–	1 × 10¹⁴	2 × 10¹²	3 × 10¹⁰	–
Vaccinia viron	10⁻¹⁵	2 × 10²	2 × 10²	4 × 10¹⁵	6 × 10¹³	9 × 10¹¹	4× 10⁹	4 × 10¹⁵	6 × 10¹³	1 × 10¹²	1 × 10¹⁰
Mycoplasma pneumoniae	10⁻¹⁴	3 × 10²	3 × 10²	2 × 10¹¹	3 × 10⁹	5 × 10⁷	3 × 10⁵	2 × 10¹¹	3 × 10⁹	6 × 10⁷	6 × 10⁵
Escherichia coli (immature)	10⁻¹³	4 × 10²	1 × 10³	2 × 10¹¹	3 × 10⁹	5 × 10⁷	3 × 10⁵	2 × 10¹¹	3 × 10⁹	6 × 10⁷	6 × 10⁵
Escherichia coli (mature)	10⁻¹²	8 × 10²	2 × 10³	2 × 10¹¹	3 × 10⁹	5 × 10⁷	3 × 10⁵	2 × 10¹¹	3 × 10⁹	6 × 10⁷	6 × 10⁵
Anthrax bacterium	10⁻¹¹	2 × 10³	6 × 10³	2 × 10¹¹	3 × 10⁹	5 × 10⁷	3 × 10⁵	2 × 10¹¹	4 × 10⁹	7 × 10⁷	7 × 10⁵
Red blood cell (human)	10⁻¹⁰	2 × 10³	8 × 10³	3 × 10¹¹	4 × 10⁹	7 × 10⁷	4 × 10⁵	3 × 10¹¹	5 × 10⁹	9 × 10⁷	9 × 10⁵
White blood cell (human)	10⁻⁹	5 × 10³	1 × 10⁴	2 × 10¹¹	3 × 10⁹	5 × 10⁷	3 × 10⁵	3 × 10¹¹	4 × 10⁹	8 × 10⁷	8 × 10⁵
Amoeba (dysentery)	10⁻⁸	2 × 10³	2 × 10⁴	1 × 10¹¹	2 × 10⁹	3 × 10⁷	2 × 10⁵	1 × 10¹¹	2 × 10⁹	4 × 10⁷	4 × 10⁵
Smooth muscle cell	10⁻⁷	1 × 10⁴	5 × 10⁵	2 × 10¹²	3 × 10¹⁰	8 × 10⁸	3 × 10⁶	3 × 10¹²	4 × 10¹⁰	8 × 10⁸	8 × 10⁶
Paramecium (protozoan)	10⁻⁶	6 × 10⁴	3 × 10⁵	7 × 10¹⁹	1 × 10¹⁸	2 × 10¹⁶	1 × 10¹⁴	9 × 10¹⁹	2 × 10¹⁸	3 × 10¹⁶	3 × 10¹⁴

Abstract

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Tables (4)

Equations (71)

Journal of the Optical Society of America B