Bi-convex solid immersion lens

Details Bi-convex solid immersion lens Bi-convex solid immersion lens

2002-01-16

2003-07-15

Sugarman, Scott J. (Department: 2873)

Optical: systems and elements

Lens

Microscope objective

C359S661000, C359S368000

Reexamination Certificate

active

06594086

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to solid immersion lenses, especially to such solid immersion lenses to increase and optimize the spatial resolution and light collection efficiency of optical imaging and collection systems.
2. Description of the Related
Optical spatial resolution is defined as the ability of an imaging system to clearly separate closely placed structures. Optical resolution is of particular importance for those who image objects in applications such as optical metrology, lithography and astronomy.
In an ideal world optical imaging elements would have infinite size where the maximum amount of light could be focused onto and/or collected from the object under investigation. The wave nature of light combined with the limited aperture of optical elements lead to diffraction—the interference of light as it scatters from the discontinuity and recombines with the light was transmitted from other areas of the optical element.
In reality optical elements are limited size and light waves diffract as they travel through these elements and recombine from the aperture of these elements. Spatial resolution in real optical systems is adversely impacted by aberrations of the optical elements with finite aperture, fields of view and their material properties, amongst other factors.
There are many elements that need to be understood and compensated to optimize the performance of an optical system. Ideally optical elements would be impervious to the different wavelengths (color) of light and thereby not impact resolution and optical performance by chromatic aberrations. Ideally these elements would also be impervious between the light transmitted and focused at the areas close to their axis (paraxial), as opposed to those transmitted and focused further from their axis. This variation for radially symmetric elements is called spherical aberration. For a review of these aberrations, amongst others, their classification, and methods to properly compensate and optimize an optical imaging system the reader may refer to classical texts on optics.
In the following we will describe an optical element and method of use to enhance and increase the resolution capabilities of high-resolution imaging with minimal aberration correction to image objects and structures embedded in the material through the sample.
Even the best optimally designed optical system where the aberrations have been properly addressed and minimized the ultimate limitation is finite aperture size of the system leading to diffraction. Therefore we will focus our attention on diffraction-limited (resolution only limited by diffraction) optical systems. Various analytical expressions have been developed to define spatial resolution in a diffraction-limited system of an optical imaging system. These formulae and expressions all relate the fundamental properties of the illuminating light and the ability of the imaging system to couple into and collect light from the sample. For example, one way to use analytical expression for the resolution is to define the lateral spatial resolving power of an optical system is to resolve a grating of period T with a lens capable of focusing and collecting light within a half-cone &thgr;
0
(
FIG. 10
a
):
T=&agr;&lgr;
0
/(
n
*sin &thgr;
0
)  (1)
Wherein &lgr;
0
is the wavelength of light in vacuum and “n” is the refractive index of the medium (i.e. for air n
0
=1, &lgr;=
0
the wavelength of light in air/vacuum. For a medium of refractive index n, &lgr;=&lgr;
0

). The proportionality constant, &agr;, is defined by the resolution criteria, i.e. &agr;=0.61 in the often-used Rayleigh resolution criterion, or &agr;=0.5 for the Sparrow resolution criterion, amongst other oft used criterion. The maximum half-angle of the cone of light relates to the numerical aperture (NA), of the lens according to:
NA=n
*sin &thgr;
0
  (2)
Therefore one obtains the relationship:
T=&agr;&lgr;
0
/(
NA
)  (3)
Consequently, efforts to increase spatial resolution have concentrated on either increasing the NA or using a light of a shorter wavelength. The NA can be increased by proper designing of the objective to increase the solid angle cone of light that is focused and collected to and from the sample, while reducing the wavelength is achieved by using a different illuminating source, for example, a laser light source or a narrow-filtered broad spectrum light source of for a shorter wavelength.
In the case where the structure under investigation is embedded in a material with an index of refraction n
1
, due to refraction, the half-cone angle inside the material (&thgr;
1
) is related through half-cone angle in air (&thgr;
0
) (
FIG. 10
b
) through the expression
n
0
Sin(&thgr;
0
)=
n
1
Sin(&thgr;
1
) (FIG.
10
b
)  (4)
Although the (sinus of the) cone angle is reduced by a factor of n
0


1
, the wavelength is also reduce by the same factor. Therefore the NA is conserved, and the effective resolution of the imaging system remains unchanged. However the off normal incident (axis) rays bending at the air-medium interface introduce spherical aberrations and axial coma, which in turn reduce the image fidelity and overall resolution.
It must also be noted that in any imaging system the ability to maximize coupling and collection light onto and from the sample under inspection is critical to the imaging performance. Since more light focused and collected from the area of interest translates into larger signal (information). When the area of interest is embedded in a material, light reflected from the sample and incident on the material-air interface outside of the critical angle (&thgr;
c
=sin
−1
(n
0


1
)) is reflected back into the sample (total internal reflection) and is not collected.
In summary, the larger the difference between the refractive indices of the imaging system and the embedded object the smaller the cone angle of focus and the higher the total internal reflection (loss of light from the sample). Therefore the goal is to reduce and compensate for the abrupt transition in refractive indices between the lensfocusing element (i.e. microscope objective) and the embedded object. The optimum would be to ‘match’ the refractive indices.
Traditionally to compensate for this reduction in resolution and collection the air gap between the objective lens and sample is filled with a fluid with a refractive index matching to that of the material, ‘index-matching fluid’. In many microscopes built for biological studies, the specimen is under a cover glass with a refractive index close (~1.5) to that of the sample. The index-matching fluid used to “bridge” between the cover-glass and embedded specimen would match as nearly as possible to the refractive indices. The objective lens in this index-matching set-up is also designed and optimized to image through the higher index fluid.
The enhancement in resolution with liquid is limited by the index of refraction of the fluid being used. The index of refraction of silicon is approximately 3.5, whereas the index of refraction of index-matching fluids is approximately 1.6. If the interface between the lens and the object is removed, then the NA of the optics can take full advantage of the higher index of refraction of transparent solid material. For example, in the case of silicon, the index of refraction is approximately 3.5. In cases where matching the refractive index of the material is not possible (for reason such as availability of fluids with matching refractive index or operational and implementation considerations), the ‘matching’ is achieved with a solid material. Obviously a primary ‘index-matching’ candidate material would be an element constructed from the same material as that of the object under study.
Although the goals are similar for solid index matching and fluid index matching (increasing the coupling and collection of light into and out of the sample) there is a major difference in

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