CC BY
96
УДК 681.784
РАЗРАБОТКА ОПТИЧЕСКОЙ СИСТЕМЫ ГРАДИЕНТНОГО ЭНДОСКОПА
Григорий Владимирович Флюдер
Варшавский политехнический университет, 00-661, Польша, Варшава, пл. Политехники, 1, кафедра инженерной фотоники, магистрант, e-mail: grzegorz.fluder@gmail.com
Алексей Валентинович Бахолдин
Университет ИТМО, 197101, Россия, г. Санкт-Петербург, Кронверкский пр., 49, кандидат технических наук, зав. кафедрой прикладной и компьютерной оптики, тел. (812)595-41-65, e-mail: bakholdin@aco.ifmo.ru
Анна Олеговна Вознесенская
Университет ИТМО, 197101, Россия, г. Санкт-Петербург, Кронверкский пр., 49, кандидат технических наук, доцент кафедры прикладной и компьютерной оптики, тел. (812)595-41-65, e-mail: voznesenskaya@mail .ifmo.ru
Работа посвящена разработке оптической системы жесткого эндоскопа, состоящей из трех элементов - объектива, транслятора и окуляра. В качестве первых двух элементов системы рассмотрены градиентные линзы. Система предназначена для визуального осмотра желудочно-кишечного тракта с дифракционным качеством изображения.
Ключевые слова: медицинские эндоскопы, жесткие эндоскопы, градиентные линзы, сапфировые наконечники.
DESIGN OF THE ENDOSCOPIC OPTICAL SYSTEM WITH THE USE OF GRADIENT INDEX LENSES
Grzegorz V. Fluder
Warsaw University of Technology, 00-661, Poland, Warsaw, pl. Polytechnics, 1, Institute of Mi-cromechanics and Photonics, master student, e-mail: grzegorz.fluder@gmail.com
Alexey V. Bakholdin
ITMO University, 197101, Russia, St. Petersburg, Kronverksky av., 49, Ph. D., Associate Professor, Head of Applied and Computer Optics Department, tel. (812)595-41-65, e-mail: bakholdin@aco.ifmo.ru
Anna O. Voznesenskaya
ITMO University, 197101, Russia, St. Petersburg, Kronverksky av., 49, Ph. D., Associate Professor, Applied and Computer Optics Department, tel. (812)595-41-65, e-mail: voznesenskaya@mail.ifmo.ru
The work is aimed to design an optical system for a rigid endoscope consisting of three main components - an objective, relay lens and eyepiece. As the first two elements gradient index lenses are used. The main purpose of the system is examining in the visible spectrum gastrointestinal tract with diffraction limited image quality.
Key words: medical endoscopes, rigid endoscopes, GRIN lenses, sapphire tips.
Introduction
Endoscopes play a big role in different fields of science, technique and medicine. They are used for observation of difficult to access objects. They are of especially big significance in diagnostics of many different illnesses - they are used among other things in bronchoscopy, arthroscopy, laryngoscopy, gastroscopy etc. For each application different factors have to be taken into account.
The endoscopic system under consideration is designed to be used in gastroscopy - the examination of the upper part of the gastrointestinal tract up to the duodenum. It is the most commonly performed endoscopic examination. It is used to diagnose many different afflictions, some of which pose a serious threat to health and life.
Since the system has to provide possibility of inspecting the gastrointestinal up to the stomach and duodenum, its length and working distance should be significant. Moreover, small diameter of the tube is crucial. The image quality of the system should be very high. Such a way, basic requirements for the system are: working distance 125 mm; angular field of view 2w=250; diameter of the lenses 2,2 mm; fully corrected coma; diffraction limited image; working in visible spectrum.
Flexible endoscopes with the use of optical fibres exist. The flexibility is certainly a significant advantage, however rigid systems offer superior image quality [1], therefore such a system has been chosen for this project. Thanks to this quality a better resolution may be obtained and therefore detecting very small changes inside of the human body is possible. Because of the inflexibility of the system, it is vital to provide as small diameter of the system as possible.
To provide compactness and simplicity of the endoscope gradient index lenses (GRIN) were considered as the objective and relay system [1-6].
In order to correct more aberrations, it is necessary to introduce more degrees of freedom. It can be done by making the surfaces of the GRIN lenses curved. In that case any four of the third-order aberrations may be corrected. In addition chromatic aberrations can also be corrected.
The schematic design of the endoscopic system is shown in Fig.2. As mentioned previously, the system consists of the objective that creates the image of the object on its rear surface, the relay lens which periodically creates intermediate images inside of it and the eyepiece.
object objective lens relay lens
f ■ intermediate image eye
Fig. 1. Schematic layout of the endoscopic system [5]
In the so far realised part of the project the objective and relay lens have been designed. The analysis has been conducted in monochromatic light.
Design of the objective
A radial GRIN lens with the entrance pupil diameter equal to 0,75 mm was designed as an objective. Additional sapphire window was introduced before the lens in order to protect the system from external factors. The aperture stop is located on the sapphire's front surface. The image is created at the back surface of the objective. The diameter of the lens is equal to 2,2 mm.
The radial gradient of the refractive index may be defined with the following well-known formula
N(r) =N0+ N±r2 + N2r4 + •••,
where N0 - on-axis refractive index; r - distance from the axis in the cross section.
By varying N0, N1, and N2 coefficients, one can obtain systems that differ not only in geometry, but also in image quality. Several designs and optical properties of the objective are presented in Fig.2-4.
The first objective (Fig.2) is rather short with a large gradient, which might be difficult to manufacture. It also does not perform well enough in terms of aberrations. Therefore other solutions have been considered.
For the second system the Airy radius is larger than in the previous case (Fig. 3). The spots for the whole field of view fall within it. There is still some amount of coma. In the next step, the N2 coefficient, the radius between the sapphire window and the lens, and the thickness of the lens have been slightly modified (Fig. 4).
For the whole field of view the image is diffraction limited. Spherical aberration, coma and astigmatism are well corrected, there is some amount of field curvature. The distortion is about 2%, which is an acceptable value. This objective was chosen for further investigation.
In the design the sapphire window with one curved surface was used. Sapphire is a hard material, but nevertheless it is possible to manufacture such curvatures with optical quality.
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Fig. 2. GRIN objective I (total length 4.72 mm, N0 = 1,629; ^ = -0,155; N2 = -4,792
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Fig. 3. GRIN objective II (total length 12 mm, N0 = 1,629; ^ = -0,018; N2 = -4,755
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Fig. 4. GRIN objective II modification (total length 12.6 mm, N0 = 1,629; Ni = -0,016; N2 = -4,070 • 10~5): a - spot diagrams, b - RMS wavefront error
Design of the relay lens
After choosing the objective, the relay lens was designed. During the process it was found that adding a thin negative GRIN lens between the objective and the relay lens enabled obtaining better results (Fig.5). Design parameters of the system are shown in the Table. Total length of the system 100 mm; gradient of the negative lens N0 = 1,629; N-l = 0,010; N2 = -5,338 • 10"3; gradient of the relay lens N0 = 1,629; Na = -0,013; N2 = -3,994 • 10"5.
The obtained system is diffraction limited within the field of view 2w=100. There is still field curvature. It was not fully corrected by the negative lens. Distortion is equal to about 1%, which is a very good value (Fig.6).
Fig. 5. Objective and relay lens
Table
Design parameters of the objective - relay lens system_
Surface Radius [mm] Thickness [mm] Material
Object 125 Infinity Air
1st (sapphire) Infinity 1 Sapphire
2nd (objective) 13,819 11,607 GRIN
3rd (negative lens) Infinity 1 GRIN
4th (relay lens) Infinity 85,388 GRIN
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b
Fig. 6. GRIN objective - relay lens system: a - spot diagrams, b - RMS wavefront error
Conclusion
The designed part of the endoscopic system does not provide satisfying image quality yet. It will be further optimized in the future to provide diffraction limited image in the whole field of view.
The system designed so far is easily manufacturable - the gradients of the refractive indices are rather small. Most of the surfaces in the system are flat, only one surface of the objective and one of the sapphire window are curved, which also makes the machining easier.
The eyepiece has to be added to make the system complete. It will be designed with the use of ordinary refractive lenses. It could compensate some of the aberrations of the previous components, which might improve the overall quality.
Finally, the chromatic aberrations have to be corrected. So far the system was examined for the monochromatic light with wavelength 0,55 ^m. The system will work in the visible spectrum, therefore it is necessary to take into account the dispersion of used optical elements.
Acknowledgment
This publication is a result of research supported by Solaris Optics S.A.
Bibliography
1. Rens Wientjes, Herke J. Noordmans, Jerine A. J. van der Eijk, Henk van den Brink Automated Objective Routine Examination of Optical Quality of Rigid Endoscopes in a Clinical Setting, PLoS ONE 8(3), e59579, doi:10.1371/journal.pone.0059579;
2. Bass M. Handbook of Optics Vol. II, McGraw-Hill, Inc., 1995. Р. 9.1-9.9;
3. Bociort F., Imaging properties of gradient-index lenses, Verlag Koester, Berlin, 1994;
4. Possner T., Messerschmidt B. GRIN micro-optical systems for mobile medical and sensor applications, SpectroNet Collaboration Forum 20.04.2011, Germany.
5. GRIN endoscopic systems, Grintech catalogue [electronic resource] -http://www.grintech.de/grin-lenses-and-lens-systems-for-imaging-optics.html;
6. Khatsevich T.N., Mikhailov I.O. Endoscopes. - Novosibirsk: SGGA, 2002. - 196 p. [electronic resource] - http://www.prooptiku.ru/endoskopy.
© Г. В. Флюдер, A. B. Бахолдин, A. О. Вознесенская, 2015
