CN111175866A - Novel long focal depth optical device with stable on-axis light intensity distribution - Google Patents
Novel long focal depth optical device with stable on-axis light intensity distribution Download PDFInfo
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- CN111175866A CN111175866A CN202010089006.6A CN202010089006A CN111175866A CN 111175866 A CN111175866 A CN 111175866A CN 202010089006 A CN202010089006 A CN 202010089006A CN 111175866 A CN111175866 A CN 111175866A
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- G—PHYSICS
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- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B5/00—Optical elements other than lenses
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- G—PHYSICS
- G02—OPTICS
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- G02B5/00—Optical elements other than lenses
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- G02B5/3083—Birefringent or phase retarding elements
Abstract
The invention discloses a novel long focal depth optical device with stable on-axis light intensity distribution, which comprises: an amplitude modulation diaphragm and a phase-type light-transmitting element; the amplitude modulation diaphragm is glued on the incident surface of the phase type light-transmitting element; the amplitude transmission coefficient of the amplitude modulation diaphragm and the thickness distribution of the phase type light-transmitting element can be obtained by reverse design of light field distribution in a long focal depth region, and a certain distribution form is met. In addition, in the amplitude modulation diaphragm, by introducing an amplitude smoothing function, the on-axis light intensity oscillation of the novel long-focus-depth optical device in a long-focus-depth area can be effectively suppressed, and a long-focus-depth function with stable on-axis light intensity distribution is obtained. The novel long-focal-depth optical device with stable on-axis light intensity distribution can solve the problem of light intensity oscillation in a long-focal-depth area, can reduce experimental processing and measurement errors, and has important application prospect in a high-precision optical system.
Description
Technical Field
The invention relates to the technical field of optics, in particular to a novel long-focus-depth optical device with stable on-axis light intensity distribution.
Background
A commonly used optical focusing device mainly comprises a lens. A conventional lens is an optical element that focuses a beam of incident light parallel to the optical axis to a point, referred to as the focal point of the lens. The prior art shows that when parallel light is incident on a conventional lens, a good focusing function can be obtained only on a predetermined focusing plane of the conventional lens. The traditional long focal depth lens refracts incident light parallel to an optical axis to different positions on the surface of the traditional long focal depth lens respectively, so that the whole long focal depth lens focuses incident plane waves to a section of range on the optical axis, and the axial long focal depth function is realized. The traditional long-focus-depth lens can realize the axial long-focus-depth function, greatly prolongs the focusing range of an optical system and widens the practical application scene. However, the conventional telephoto lens has an obvious defect that the on-axis light intensity oscillates in the telephoto region, and the relative error of the on-axis light intensity is about 15% to 20%, which brings about large experimental processing and measurement errors and limits the application of the lens in a high-precision optical system.
Disclosure of Invention
In view of the above, the present invention is directed to a novel optical device with a long focal depth and a stable on-axis light intensity distribution, which can solve the problem of on-axis light intensity oscillation in the long focal depth region.
In view of the above, the present invention provides a novel long-focus optical device with stable on-axis light intensity distribution, comprising: an amplitude modulation diaphragm and a phase-type light-transmitting element; the amplitude modulation diaphragm is glued on the incident surface of the phase type light-transmitting element.
For the phase type light transmission element, the thickness of the phase type light transmission element satisfies the following formula:
wherein r denotes a radial position coordinate of the phase type light-transmitting element on a cross section perpendicular to the optical axis, λ denotes a wavelength of the incident plane wave in vacuum, n1And n2Respectively representing the refractive indices of the phase-type light-transmitting element and the external space,
expressing the phase distribution of the phase type light-transmitting elementComprises the following steps:
wherein arg [ E (r) ] represents the argument of the complex function E (r). In the above formula, the optical field distribution E (r) at any point on the exit surface of the phase-type light-transmitting element is:
wherein r represents a radial position coordinate of the phase-type light-transmitting element on a cross section perpendicular to the optical axis,
is an imaginary unit, n2λ is the wavelength of an incident plane wave in vacuum, z represents the longitudinal position coordinate of any point on the optical axis, z1And z2Respectively representing the coordinate values of the initial position and the final position of the long focal depth area along the optical axis direction, and respectively calculating formulas as follows:
wherein f is0And Δ f represent the initial focal length and the depth of focus of the novel long-depth-of-focus optical device, respectively, and ε is the depth of focus expansion coefficient.
The amplitude transmission coefficient of the amplitude modulation diaphragm is as follows:
T(r)＝||E(r)||·T0(r),
where E (r) represents the modulus of the complex function E (r), T0(r) is given by:
wherein eta is an amplitude smoothing coefficient, the value range of eta is more than 0 and less than or equal to 1, and R is the radius of the amplitude modulation diaphragm.
In some other embodiments, the radius of the amplitude modulation aperture is: r is 12.5 mm.
In some other embodiments, the refractive index of the phase-type light-transmitting element is: n is1＝1.5。
In some other embodiments, the refractive index of the external space is: n is2＝1。
In some other embodiments, the wavelength of the incident plane wave in the vacuum is: λ 633 nm.
In other embodiments, the initial focal length of the novel long depth of focus optical device is: f. of0＝1220mm。
In other embodiments, the depth of focus is: Δ f ═ 29 mm.
In some other embodiments, the depth of focus extension coefficient: ε is 1.5.
in other embodiments, η ═ 0.35 is applied to the amplitude smoothing coefficient.
From the above, it can be seen that the present invention provides a novel long-focus optical device with stable on-axis light intensity distribution, comprising: an amplitude modulation diaphragm and a phase-type light-transmitting element; the amplitude modulation diaphragm is glued on the incident surface of the phase type light-transmitting element. The thickness of the phase type light-transmitting element and the amplitude transmission coefficient of the amplitude modulation diaphragm are respectively designed according to the function distribution, so that the novel long focal depth optical device with stable on-axis light intensity distribution can solve the problem of light intensity oscillation in a long focal depth area, reduce experimental processing and measurement errors, and has wide application in a high-precision optical system.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic illustration of conventional lens focusing;
FIG. 2 is a schematic diagram of conventional tele depth lens focusing;
FIG. 3 is a schematic illustration of the focusing of a novel long depth of focus optical arrangement with a stable on-axis light intensity distribution according to an embodiment of the present invention;
FIG. 4 is a normalized on-axis light intensity profile for a conventional lens, a conventional tele depth lens, and a novel tele depth optical device with a stable on-axis light intensity profile of an embodiment of the present invention;
FIG. 5 is a graph of intensity distribution over different cross-sections in a long depth of focus region for a novel long depth of focus optical device in accordance with embodiments of the present invention;
FIG. 6 is a graph of intensity distribution over different cross-sections of a conventional tele depth lens in the tele depth region.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
It is to be noted that technical terms or scientific terms used in the embodiments of the present invention should have the ordinary meanings as understood by those having ordinary skill in the art to which the present disclosure belongs, unless otherwise defined. The use of "first," "second," and similar terms in this disclosure is not intended to indicate any order, quantity, or importance, but rather is used to distinguish one element from another. The word "comprising" or "comprises", and the like, means that the element or item listed before the word covers the element or item listed after the word and its equivalents, but does not exclude other elements or items. The terms "connected" or "coupled" and the like are not restricted to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "upper", "lower", "left", "right", and the like are used merely to indicate relative positional relationships, and when the absolute position of the object being described is changed, the relative positional relationships may also be changed accordingly.
Referring to fig. 1, in the conventional art, a conventional lens is an optical element that focuses a beam of an incident plane wave parallel to an optical axis to a point, the incident direction of the plane wave is a positive z-axis direction, and the conventional lens is placed on a plane where z is 0. Thus, all points on the surface of a conventional lens are intended to be focused on the same point, i.e. the focal point of the conventional lens. According to the principle of interference enhancement in wave optics, the thickness function of a conventional lens satisfies the following formula:
wherein r ' represents a radial position coordinate, n ', of any point on the surface of the conventional lens on a cross-section perpendicular to the optical axis '1And n2Respectively, the refractive indexes of the conventional lens and the external space, R 'represents the radius of the conventional lens, and f' represents the focal length of the conventional lens.
The prior art shows that in the conventional lens, good focusing performance can be obtained only on the predetermined focusing plane, and even if the actual detection plane has a small position deviation from the predetermined focusing plane, the focusing performance of the conventional lens is reduced sharply, which limits many applications of the conventional lens in practical optical systems.
In view of this, the conventional lens is further improved to obtain a conventional telephoto lens. The direction of the incident plane wave is the positive direction of the z-axis, and the conventional long-focus depth lens is placed on the plane where z is 0, as shown in fig. 2. In the traditional long-focus depth lens, the incident plane waves parallel to the z axis are respectively refracted to different positions on the z axis by different positions on the surface of the traditional long-focus depth lens, so that the whole long-focus depth lens can focus the incident plane waves in a section of range on the optical axis, and the long-focus depth function of the traditional long-focus depth lens is realized.
According to the wave optics principle, the thickness function of a conventional telephoto lens satisfies the following formula:
wherein r' represents an arbitrary point on the surface of the conventional telephoto lens in a cross section perpendicular to the optical axisRadial position coordinate, n ″)1And n2Respectively, the refractive indices of the conventional telephoto lens and the external space, R' represents the radius of the conventional telephoto lens, f ″)0And Δ f "represent the initial focal length and depth of focus magnitude, respectively, of a conventional telephoto lens.
The prior art shows that the traditional long-focus depth lens can realize the axial long-focus depth function, greatly prolongs the focusing range of an optical system, reduces the requirement on the stability of the optical system and widens the practical application scene. However, the conventional telephoto lens has an obvious defect that the on-axis light intensity in the telephoto region has an oscillation problem, and the light intensity error is about 15% to 20%, which brings large errors to experimental processing and measurement and limits the application of the lens in a high-precision optical system.
In view of the above, the present invention provides a novel long-focus depth optical device with stable on-axis light intensity distribution, referring to fig. 3, comprising: an amplitude modulation diaphragm 1 and a phase-type light-transmitting element 2. The amplitude modulation diaphragm 1 is glued to the entrance face of the phase-type light-transmitting element 2, and the two elements are structurally matched with each other to form a glued long-focus-depth optical device as a whole. The incident plane wave enters the amplitude modulation aperture 1 from left to right, passes through the incident surface of the phase type light transmitting element 2, and is transmitted through the exit surface of the phase type light transmitting element 2. The incident direction of the plane wave is the positive direction of the z axis, and the phase-type light-transmitting element 2 is arranged on the plane where z is 0.
According to the huygens-fresnel principle, the light field at each observation point in the long focal depth region of the novel long focal depth optical device proposed in this embodiment is formed by diffracting and superposing the light fields of all source points on the exit surface of the phase-type light-transmitting element 2. According to the principle of inverse diffraction, the light field of any point on the exit surface of the phase type light-transmitting element 2 can be inversely designed by the light fields of all observation points in the long focal depth region. Therefore, the thickness of the phase-type light-transmitting element 2 can be designed according to the light field at each observation point in the long depth of focus region of the novel long depth of focus optical device. Specifically, for the phase type light transmission element 2, the thickness h (r) thereof satisfies the following formula:
where r denotes the radial position coordinate of the novel tele-depth optical arrangement on a cross-section perpendicular to the optical axis, λ denotes the wavelength of the incident plane wave in vacuum, n1And n2Respectively representing the refractive indices of the phase-type light-transmitting element 2 and the external space,
the phase distribution of the phase type light transmission element 2 is expressed by:
wherein arg [ E (r) ] represents the argument of the complex function E (r). In formula (4), the optical field distribution E (r) at any point on the exit surface of the phase-type light-transmitting element 2 is:
wherein r is the radial position coordinate of the novel long focal depth optical device on the cross section vertical to the optical axis,
is an imaginary unit, n2λ is the wavelength of an incident plane wave in vacuum, z represents the longitudinal position coordinate of any point on the optical axis, z1And z2Respectively representing the coordinates of the initial position and the ending position of the long focal depth area along the optical axis direction, and the calculation formulas are respectively as follows:
wherein f is0And Δ f represent the initial focal length and the depth of focus of the novel long-depth-of-focus optical device, respectively, and ε is the depth of focus expansion coefficient.
The amplitude transmission coefficient of the amplitude modulation diaphragm 1 is as follows:
T(r)＝||E(r)||·T0(r). (7)
it can be seen that the amplitude transmission coefficient of the amplitude modulation aperture 1 is related to the optical field distribution E (r) on the exit surface of the phase-type light-transmitting element 2, that is, the amplitude modulation aperture 1 and the phase-type light-transmitting element 2 cooperate with each other to complete the novel long-focus-depth optical device proposed in this embodiment. In equation (7), the amplitude smoothing function T is introduced into the amplitude modulation diaphragm 10(r) the light intensity oscillation in the long focal depth region of the proposed novel long focal depth optical device can be effectively suppressed, and the long focal depth function of stabilizing the light intensity distribution on the axis can be obtained. Wherein the amplitude smoothing function T0(r) is given by:
wherein η is an amplitude smoothing coefficient, the value range of η is more than 0 and less than or equal to 1, and R is the radius of the amplitude modulation diaphragm 1.
To further illustrate the technical effect of the solution of the embodiment of the present invention, the inventors selected a set of parameters and performed numerical simulations. The specific parameters include: radius of amplitude modulation diaphragm: r — 12.5mm, refractive index of the phase type light-transmitting element: n is11.5, refractive index of outer space: n is21, wavelength of incident plane wave in vacuum: λ 633nm, initial focal length of the novel long depth of focus optical device: f. of0the focal depth is equal to 1220mm, the f is equal to 29mm, the expansion coefficient of the focal depth is equal to 1.5, the amplitude smoothing coefficient is equal to 0.35, for the convenience of comparison, the inventor selects a group of parameters, and the focusing performance of the traditional telephoto depth lens and the focusing performance of the conventional lens are simulated and calculated respectively0The focal depth of a traditional telephoto lens is: Δ f ″, 29mm, the refractive indices of both conventional telephoto and conventional lenses are: n ″)1＝n′11.5 refraction of the outer spaceThe ratio is: n is2＝1。
The on-axis intensity distribution of the transmission area was calculated by simulation using the strict rayleigh-sommerfen method according to the parameters selected above, as shown in fig. 4.
In fig. 4, the solid line, the broken line, and the chain-dotted line represent on-axis normalized light intensity distributions of the novel long-focus-depth optical device, the conventional long-focus-depth lens, and the conventional lens, respectively. As can be seen from fig. 4, the novel long-focus-depth optical device realizes stable on-axis light intensity distribution in a relatively long region on the optical axis, and the numerical calculation result shows that the relative error of the on-axis light intensity in the long-focus-depth region is less than 1%, as shown by the solid line in fig. 4; for the conventional telephoto lens, although the function of telephoto depth on the optical axis can also be achieved, the light intensity distribution in the telephoto depth region has an obvious oscillation effect, and the relative error of the light intensity on the axis is greater than 15%, as shown by the dotted line in fig. 4; with the conventional lens, the width of the focusing area in the optical axis direction is small, and the axial long-focus-depth function is not provided, as shown by the chain line in fig. 4.
In addition, to further characterize the stability of the lateral focusing performance of the novel tele-depth optical device in the tele region, the intensity distribution over a number of cross-sections perpendicular to the optical axis was calculated by simulation using the strict rayleigh-sommerfen method, as shown in fig. 5. For comparison, the intensity distribution of the conventional telephoto lens over a plurality of cross sections in the telephoto region is also calculated, as shown in fig. 6.
As can be seen from fig. 5, the novel long-focus-depth optical device designed by the present invention has good focusing characteristics in the range from 1223mm to 1243mm in the long-focus-depth region, most of the incident energy is focused in the range of the central light spot, the focusing efficiency is high, the background noise is low, and in addition, the light intensity distributions on different cross sections are almost overlapped, which indicates that each cross section has stable focusing performance in the whole long-focus-depth region. As can be seen from fig. 6, for the conventional telephoto lens, the difference between the peak light intensity and the spot size at different cross sections is large in the range of 1240mm to 1260mm in the telephoto region, indicating that the focusing characteristics at different cross sections are unstable throughout the entire telephoto region of the conventional telephoto lens.
In summary, the present embodiment provides a novel long-focus-depth optical device, which realizes a stable long-focus-depth function on an optical axis, and maintains a stable focusing characteristic on a cross section in the entire long-focus-depth region; and the thickness of the phase type light-transmitting element can be obtained through the light field distribution design at all observation points in the long focal depth region.
Those of ordinary skill in the art will understand that: the discussion of any embodiment above is meant to be exemplary only, and is not intended to intimate that the scope of the disclosure, including the claims, is limited to these examples; within the idea of the invention, also features in the above embodiments or in different embodiments may be combined, steps may be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity.
The embodiments of the invention are intended to embrace all such alternatives, modifications and variances that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, substitutions, improvements and the like that may be made without departing from the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (9)
1. A novel long depth of focus optical device having a stable on-axis light intensity distribution, comprising: an amplitude modulation diaphragm and a phase-type light-transmitting element; the amplitude modulation diaphragm is glued on the incident surface of the phase type light-transmitting element;
for the phase type light transmission element, the thickness thereof satisfies the following formula:
wherein r represents the radial position coordinate of the novel long-focus-depth optical device on a cross section perpendicular to the optical axis, λ represents the wavelength of the incident plane wave in vacuum, and n1And n2Respectively representing the refractive indices of the phase-type light-transmitting element and the external space,
the phase distribution of the phase type light-transmitting element is expressed by the following expression:
wherein arg [ E (r) ] represents the argument of the complex function E (r); the optical field distribution E (r) at any point on the emergent surface of the phase type light-transmitting element is as follows:
wherein r represents the radial position coordinate of the novel tele-depth optical device on a cross-section perpendicular to the optical axis,
is an imaginary unit, n2Denotes a refractive index of an external space, λ denotes a wavelength of an incident plane wave in a vacuum, z denotes a longitudinal position coordinate of any point on an optical axis, and z1And z2Respectively representing the coordinates of the initial position and the ending position of the long focal depth area along the optical axis direction, and the calculation formulas are respectively as follows:
wherein f is0And Δ f respectively represent the initial focal length and the focal depth of the novel long-focal-depth optical device, and ε is the focal depth expansion coefficient;
the amplitude transmission coefficient of the amplitude modulation diaphragm is as follows:
T(r)＝||E(r)||·T0(r)
wherein, | | E (r) | | represents solving a modulus of the complex function E (r); to obtain a stable on-axis light intensity distribution, an amplitude smoothing function T is introduced into the amplitude modulation diaphragm0(r) is given by:
wherein eta is an amplitude smoothing coefficient, the value range of eta is more than 0 and less than or equal to 1, and R is the radius of the amplitude modulation diaphragm.
2. The novel long depth of focus optical device of claim 1, having a stable on-axis light intensity distribution,
radius of the amplitude modulation diaphragm: r is 12.5 mm.
3. The novel long depth of focus optical device of claim 1, having a stable on-axis light intensity distribution,
refractive index of the phase type light transmitting element: n is1＝1.5。
4. The novel long depth of focus optical device of claim 1, having a stable on-axis light intensity distribution,
refractive index of the external space: n is2＝1。
5. The novel long depth of focus optical device of claim 1, having a stable on-axis light intensity distribution,
wavelength of the incident plane wave in vacuum: λ 633 nm.
6. The novel long depth of focus optical device of claim 1, having a stable on-axis light intensity distribution,
initial focal length of the long focal depth region: f. of0＝1220mm。
7. The novel long depth of focus optical device of claim 1, having a stable on-axis light intensity distribution,
the depth of focus is: Δ f ═ 29 mm.
8. The novel long depth of focus optical device of claim 1, having a stable on-axis light intensity distribution,
the depth of focus expansion coefficient: ε is 1.5.
9. The novel long depth of focus optical device of claim 1, having a stable on-axis light intensity distribution,
and eta of the amplitude smoothing coefficient η is 0.35.
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