CN101299079A - Invisible apparatus and design based on geometrical optics - Google Patents

Abstract

The present invention provides a concealing device which is based on geometric optics and a design thereof, and relates to the field of optical concealing technique. According to the principle of physical optics, the light beams are converged with a convex lens. The cross-sectional area of the light beam is changed. The incidence light at the front of the object can be converged through the convex lens and transferred to the backside of the object through an image transferring channel, and is changed to the former incidence ray through radiation. The effect of concealing the visible light is obtained. The core of the device is that the concealing device is composed of at least one group of object group 1 which can be permeated with light and focus the light, a light beam transmission component 2 which is provided between the focusing object group 1 and a concealing area 3. The device is designed with an imaging formula of the convex lens to obtain the effect of optical concealing the visible light. The concealing state of the device is sustained without exterior power. The exterior exposed part of the device is fewer. Compared with the optical physical concealing device, the concealing device according to the invention has the characteristics of simple structure, easy manufacture, low cost and wide application area.

Description

A kind of hidden apparatus and design thereof based on geometrical optics

Technical field

The present invention relates to optics stealth technique field, specifically refer to a kind of hidden apparatus and design based on geometrical optics.

Background technology

Modern stealth technique has good development and application in fields such as infrared, radar, sonars.By be coated with the last layer certain material at body surface, make it produce strong the absorption at specific band, just can reach the effect of evading detection.Such as, on aircraft or submarine, to coat and can block ultrared material, infrared eye just is difficult to detect its existence.But at visible light (wavelength is the electromagnetic wave between 380 to 780 nanometers greatly) wave band, stealth technique still has the space of developing on a large scale very much.Many in the world scientists are being engaged in the research in this field at present, for example:

(1) professor of Tokyo Univ Japan " invisible clothes " vision camouflage is by the image line holographic projections with the back.Principle is that the scene with the clothes back is filmed by video camera, then with image transitions to the projector of clothes front, again image is projected on the dress material of being made by special material.

(2) Russian Ulyanovsk state university adds professor Mu Siji and has claimed to invent out a kind of special " invisible clothes ".Add professor Mu Siji and find, an object just can reach stealthy effect as long as cover upward a kind of " special coat " of being made by the gold colloidal particle.

(3) according to American Media, scientist develops global initial workpiece two dimension " invisible clothes ".The main material of this part " invisible clothes " is the potpourri of metal and circuit board material, this material can absorb specific light, the special material that uses can allow radar wave, light or other ripple walk around object and can not rebound, and then reach not visible effect.A few days ago, the U.S. and Britain two countries scientist utilizes optical principle, successfully uses it " stealthy " a copper coin cylinder.This great discovery is published on " science " magazine.

This shows, more than all be based on the stealthy mode of optical physics principle, or the vision of photovoltaic principals camouflage.Have complex structure, material requirements is special, uses deficiencies such as adding light source.

Summary of the invention

The deficiency that purpose of the present invention exists for the solution prior art, and a kind of hidden apparatus based on geometric optical theory that is different from prior art is proposed.Conceptual design based on above-mentioned analysis the present invention proposition: in object the place ahead, the light that may incide object is assembled by convex lens, as channel, be delivered to the object rear via a kind of biography, the light beam that will be assembled is reduced into original incident ray by another piece convex lens again.Object is not shone by light like this, and the observer can only see the optical imagery in object the place ahead, and can't see object, thereby reach the two-dimensional invisible effect at the rear of object.

The innovative point of this device is that at least one group can allow light see through by one and the articles of its focusing and several parts of beam Propagation parts and stealthy district of being arranged between the articles of this focusing are constituted.

One of hidden apparatus design proposal

When a branch of directional light shines the place ahead, object front, it is converged to tiny light beam injects image transmission optical fibre one end, then by image transmission optical fibre (step change type fibre bundle) transmission, (because optical fiber is flexible can curve arbitrary shape, make it from object the place ahead around to the object rear) at the other end of image transmission optical fibre, the light beam of assembling is penetrated, and makes it diverge to directional light, final imaging reaches stealthy effect (as shown in Figure 1).

Two of hidden apparatus design proposal

Improve its beam Propagation part, plate a silverskin (shown in the accompanying drawing 2a), to realize utilizing the principle of reflection transmitting beam at a thinner inner wall of metal tube of caliber.Direct reflection can reach 100% reflectivity in theory, thus the luminance brightness of equivalence before and after obtaining.Because the reflectivity of silver-colored film reaches more than 98%, plans this preferred material as reflectance coating.

Analyzed as can be known by principle of work (shown in the accompanying drawing 2b): the parity of the order of reflection n of light beam in the reflection tube directly final imaging of influence is erect image or inverted image.In view of the above, { n|n=2x+1 during x ∈ N*} (odd number), becomes erect image as n ∈; Otherwise { n|n=2x during x ∈ N*} (even number), becomes inverted image as n ∈.

Length L, reflection tube inside radius r, the radius R of convex lens and the length f relevant (shown in accompanying drawing 2c) of one times of focal length of order of reflection n and reflection tube in this programme.Because of the θ angle equates to obtain R/f=r/x, thus x=fr/R, and L=2nx derives relational expression thus:

n＝LR/2fr

Three of hidden apparatus design proposal

Beam Propagation partly replaces optical fiber or reflection tube (shown in accompanying drawing 3a) with lens

Wherein, handle about the stealth of directional light

At first, a planoconvex lens is assembled a branch of directional light, by the biconvex mirror group light beam symmetry of assembling is transmitted, and disperses by the identical planoconvex lens of another piece again.Find that when the research index path biography is erect image or inverted image as the final imaging of the direct influence of the parity of the number n of the biconvex lens of channel.{ n|n=2x+1 during x ∈ N} (odd number), becomes erect image as n ∈.{ n|n=2x during x ∈ N*} (even number), becomes inverted image (shown in accompanying drawing 3b) as n ∈

3b and accompanying drawing 3c analyze in conjunction with the accompanying drawings, and the scioptics a of directional light elder generation focuses on 1 times of focal length place, is again lens b two focus length place (shown in Fig. 3 b) herein.Because θ=α,, obtain formula thus so 1/2 diameter of lens a equals two times of focal lengths of 1/2 diameter of lens b than lens b than one times of focal length of lens a:

Ra/2fa＝rb/4fb

Stealthy Treatment Analysis about non-parallel light

Occurring in nature, many visible light beams are not directional light, therefore in visible light optics hidden apparatus, handling the non-parallel light time, should to do corresponding the adjustment be that the position of lens will change according to the distance (be object distance) of light source apart from lens, and the position of lens can be by the convex lens imaging formula: 1. 1/u+1/v=1/f derives and get.

In sum, can allow light see through by one and with the articles of its focusing be arranged at the device that several parts of beam Propagation parts and stealthy district between the articles of this focusing constitute, utilize the geometrical optics principle to reach the effect of the optics stealth of visible light by at least one group of the present invention; Do not need the extra power supply during holdout device stealth state; The outer exposed part of device is less; Have simple in structurely than the optical physics hidden apparatus, easily produce, but the characteristics of with low cost and widespread use.

Description of drawings

Fig. 1 is the embodiment of the invention 1 schematic diagram;

Fig. 2 a is the embodiment of the invention 2 beam Propagation parts 2 structural representations;

Fig. 2 b is the embodiment of the invention 2 beam Propagation parts 2 schematic diagrams;

Fig. 2 c is the embodiment of the invention 2 beam Propagation parts 2 computational analysis figure;

Fig. 3 a is the embodiment of the invention 3 structural representations;

Fig. 3 b is one of the embodiment of the invention 3 beam Propagation parts 2 computational analysis figure;

Fig. 3 c is two of the embodiment of the invention 3 beam Propagation parts 2 computational analysis figure;

Fig. 3 d is one of the embodiment of the invention 3 imaging design diagrams;

Fig. 3 e is one of the embodiment of the invention 3 imaging design diagrams;

Fig. 3 f is two of the embodiment of the invention 3 imaging design diagrams;

Fig. 3 g is two of the embodiment of the invention 3 imaging design diagrams;

Fig. 3 h is the embodiment of the invention 4 structural representations;

Fig. 3 i is one of the embodiment of the invention 4 imaging design diagrams

Fig. 3 j is two of the embodiment of the invention 4 imaging design diagrams.

Embodiment

Below in conjunction with accompanying drawing the present invention is further described:

A kind of hidden apparatus based on geometric optical theory, at least one group can allow light see through by one and the articles 1 of its focusing and the beam Propagation parts 2 and stealthy district more than 3 parts that are arranged at 1 of the articles of this focusing are constituted; Wherein, described articles 1 is the convex lens of a plating anti-reflection film, perhaps is the positive balsaming lens of achromatism of a plating anti-reflection film, perhaps is a zone plate.

The calculation Design of a kind of hidden apparatus based on geometric optical theory of the present invention

Stealthy volume size V=S1*L1-2/3*S1*f-S2* (L1-2f) wherein,

S1: but the cross-sectional area of both sides focused ray lens 1;

L1: but the spacing of both sides focused ray lens 1;

F: but the focal length of both sides focused ray lens 1;

S2: the cross-sectional area of beam Propagation parts 2.

Described lens (4) are pressed directional light design formula: Ra/fa=Rb/2fb

Wherein, Ra: the radius of lens a;

Rb: the radius of lens b;

Fa: one times of focal length of lens a;

Fb: one times of focal length of lens b;

Apparatus of the present invention embodiment 1

At least one group can allow light see through by one and the articles 1 of its focusing and the beam Propagation parts 2 and stealthy district more than 3 parts that are arranged at 1 of the articles of this focusing are constituted.Wherein, the articles 1 of described light focusing is a plano-convex lens group, and described beam Propagation parts are an optical fiber.

When a branch of directional light shines the place ahead, object front, it is converged to tiny light beam injects image transmission optical fibre one end, then by image transmission optical fibre (step change type fibre bundle) transmission, (because optical fiber is flexible can curve arbitrary shape, make it from object the place ahead around to the object rear) at the other end of image transmission optical fibre, the light beam of assembling is penetrated, and makes it diverge to directional light, final imaging reaches stealthy effect (as shown in Figure 1).

Present embodiment, the articles 1 of described light focusing also can adopt a thin thickness, light weight, easily the zone plate group of producing.

Apparatus of the present invention embodiment 2

Can allow light see through and the articles 1 of its focusing and the beam Propagation parts 2 and stealthy district more than 3 parts that are arranged at 1 of the articles of this focusing are constituted by one.Wherein, the articles 1 of described light focusing adopts a plano-convex lens group, and described beam Propagation parts 2 are a silverskin reflection tube.Wherein, silverskin reflection tube structure is shown in accompanying drawing 2a; Principle of work is shown in accompanying drawing 2b.

Apparatus of the present invention embodiment 3

At least one group can allow light see through by one and the articles 1 of its focusing and the beam Propagation parts 2 and stealthy district more than 3 parts that are arranged at 1 of the articles of this focusing are constituted.Wherein, the articles 1 of described light focusing adopts a plano-convex lens group, and described beam Propagation parts 2 are an odd number piece biconvex lens (lens 4) (shown in accompanying drawing 3a).

About lens (4) is one of odd number piece biconvex lens imaging design

Present embodiment, lens (4) be set to 1 biconvex lens

1 biconvex lens imaging design (shown in accompanying drawing Fig. 3 d)

If: lens 1 are (V1+U2) with the spacing of lens 2, U2=2f2; Lens 2 are (V2+U3) with the spacing of lens 3

Wherein,

F1: one times of focal length of lens 1; (f1=f3)

F2: one times of focal length of lens 2;

U1: the object distance of lens 1;

V1: the image distance of lens 1;

U2: the object distance of lens 2;

V2: the image distance of lens 2;

U3: the object distance of lens 3;

V3: the image distance of lens 3;

1. general introduction: the light that object reflects is through 1 one-tenth real image that stands upside down and dwindle of lens, image position is in one times of focal length of lens 2, this real image sees through lens 2 and becomes the virtual image with respect to original handstand between lens 1 and lens 2, and this virtual image is again through 3 one-tenth on lens and the upright real image that equates of the original.

2. the position between lens concerns: lens 1 are (V1+U2) with the spacing of lens 2, U2＜f2; Lens 2 are (U3-V2) with the spacing of lens 3.Wherein, lens 1 should be greater than lens 2 with the diameter of lens 3, and lens 1 are identical with lens 3, constitute an articles 1.

3. imaging analysis: in this lens combination, what must have that lens become is the virtual image.Final like this imaging is a upright picture, 2 one-tenth virtual images of lens in accompanying drawing 3b, so U2＜f2.Since amplify during the virtual image, U3 ≠ V1, U1 ≠ V3, otherwise final imaging will be greater than the original.For so big picture such as become, (1) U3 ∈ (2f3 ,+∞), the virtual image is greater than the original, just like this may be behind lens 3 (f3 dwindles in scope 2f3) and big real images such as the original.(2) U3 ∈ (f3,2f3), the virtual image is less than the original, so just may be behind lens 3 (2f3 zooms into and big real images such as the original in+∞) the scope.

4. conclusion: shown in the accompanying drawing 3d, have the amphicheirality.

Wherein, design formula:

If U ₁=x S ₄=S ₁=a V ₃=y (x, y all＞f ₁)

${\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">V</figure-callout>}}_1=\frac{f_1{U}_1}{U_1-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}=\frac{f_{1}x}{x-f_1}$ ${\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">S</figure-callout>}}_2=\frac{V_1}{U_1}{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">S</figure-callout>}}_1=\frac{f_{1}a}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}$ In like manner: ${\mathrm{<figure-callout\; id="3"\; label="S"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">S</figure-callout>}}_3=\frac{f_{1}a}{y-f_1}$ ${\mathrm{<figure-callout\; id="3"\; label="U"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">U</figure-callout>}}_3=\frac{f_{1}y}{y-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}$ $\underset{\&CenterDot;}{\&CenterDot;\&CenterDot;}\frac{S_2}{{\mathrm{<figure-callout\; id="3"\; label="S"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">S</figure-callout>}}_3}=\frac{U_2}{{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">V</figure-callout>}}_2}$ $\stackrel{\&CenterDot;}{\&CenterDot;\&CenterDot;}\frac{y-f_1}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}=\frac{U_2}{{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">V</figure-callout>}}_2}$

If U ₂=(y-f ₁) k V ₂=(x-f ₁) k

$\underset{\&CenterDot;}{\&CenterDot;\&CenterDot;}\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}=\frac{1}{U_2}-\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">V</figure-callout>}}_2}$ $\stackrel{\&CenterDot;}{\&CenterDot;\&CenterDot;}\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}=\frac{1}{k}(\frac{1}{y-f_1}-\frac{1}{x-f_1})$ $\stackrel{\&CenterDot;}{\&CenterDot;\&CenterDot;}k=\frac{x-y}{(x-f_1)(y-f_1)}{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">f</figure-callout>}}_2$ $\stackrel{\&CenterDot;}{\&CenterDot;\&CenterDot;}{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">U</figure-callout>}}_2=\frac{x-y}{x-f_1}{f}_2$ ${\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">V</figure-callout>}}_2=\frac{x-y}{y-f_1}{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">f</figure-callout>}}_2$

${\mathrm{<figure-callout\; id="12"\; label="L"\; filenames="A20081003732700322.png"\; state="\{\{state\}\}">L</figure-callout>}}_{12}=\frac{f_{1}x+f_2(x-y)}{x-f_1}$ $L_{23}=U_3-{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">V</figure-callout>}}_2=\frac{f_{1}y-f_2(x-y)}{y-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}$

If must have the amphicheirality, then ${\mathrm{<figure-callout\; id="12"\; label="L"\; filenames="A20081003732700322.png"\; state="\{\{state\}\}">L</figure-callout>}}_{12}=L_{23}\&DoubleRightArrow;x$ Should satisfy with y: $\frac{f_{1}x+f_2(x-y)}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}=\frac{f_{1}y-f_2(x-y)}{y-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}$

Present embodiment, lens 4 be set to n ∈ { n|n=2x+1, x ∈ N ^*1 above odd number piece biconvex lens imaging design of odd number piece biconvex lens (shown in accompanying drawing 3e)

If: lens 1 are (V1+U2+4fz (n-1)) with the spacing of lens 2, U2=2f2; Lens 2 are (V2+U3) with the spacing of lens 3

Between the lens 1 of 1 biconvex lens imaging and biconvex lens 2, increase the biconvex lens number in pairs.And the spacing that makes real image that lens 1 become and newly-increased biconvex lens 11 is to be (2fz+U2) between newly-increased biconvex lens 1 (n-1) of 2fz and the lens 2; Make the spacing of newly-increased biconvex lens 11 and newly-increased biconvex lens 12 ... be 4fz to reaching the spacing of newly-increased biconvex lens 1 (n-2) with newly-increased biconvex lens 1 (n-1).Not change the mentality of designing of 1 biconvex lens imaging scheme, the purpose of real image that symmetrical relay len 1 becomes.The focal distance f z of newly-increased biconvex lens can be identical with the focal length of biconvex lens 2.

Wherein,

F1: one times of focal length of lens 1;

F2: one times of focal length of lens 2;

Fz: one times of focal length of newly-increased lens;

U1: the object distance of lens 1;

V1: the image distance of lens 1;

U2: the object distance of lens 2;

V2: the image distance of lens 2;

U3: the object distance of lens 3;

V3: the image distance of lens 3;

L12: the spacing of lens 1 and lens 2;

L23: the spacing of lens 2 and lens 3;

L03: the distance apart from lens 3 in kind.

Wherein, design formula:

If U ₁=x S ₄=S ₁=a V ₃=y (x, y all＞f ₁)

${\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">V</figure-callout>}}_1=\frac{f_1{U}_1}{U_1-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}=\frac{f_{1}x}{x-f_1}$ ${\mathrm{<figure-callout\; id="3"\; label="U"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">U</figure-callout>}}_3=\frac{f_{1}y}{y-f_1}$ ${\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">U</figure-callout>}}_2=\frac{x-y}{x-f_1}{f}_2$ ${\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">V</figure-callout>}}_2=\frac{x-y}{y-f_1}{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">f</figure-callout>}}_2$

${\mathrm{<figure-callout\; id="12"\; label="L"\; filenames="A20081003732700322.png"\; state="\{\{state\}\}">L</figure-callout>}}_{12}=\frac{f_{1}x+f_2(x-y)}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}+4f_z(n-1)$ $L_{23}=U_3-{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">V</figure-callout>}}_2=\frac{f_{1}y-f_2(x-y)}{y-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}$

If must have the amphicheirality, x and y still satisfy: $\frac{f_{1}x+f_2(x-y)}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}=\frac{f_{1}y-f_2(x-y)}{y-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}$

About lens (4) is odd number piece biconvex lens imaging design two

Present embodiment, lens 4 be set to 1 biconvex lens

1 biconvex lens imaging design (shown in accompanying drawing 3f)

If: lens 1 are (V1+U2) with the spacing of lens 2, U2=2f2; Lens 2 are (V2+U3) with the spacing of lens 3

Wherein,

F1: one times of focal length of lens 1;

F2: one times of focal length of lens 2;

U1: the object distance of lens 1;

V1: the image distance of lens 1;

U2: the object distance of lens 2;

V2: the image distance of lens 2;

U3: the object distance of lens 3;

V3: the image distance of lens 3;

L12: the interval of lens 1 and lens 2;

L23: the interval of lens 2 and lens 3;

L03: the distance apart from lens 3 in kind.

1. general introduction: the light that object reflects is through 1 one-tenth real image that stands upside down and dwindle of lens, and image position is in two times of focal length places of lens 2, and this inverted real image sees through 2 one-tenth upright real images of the relative original of lens, is positioned at one times of focal length of lens 3.This upright real image sees through lens 3 again, becomes to equate and the upright virtual image with the original, is positioned at former place in kind.

2. the position between lens concerns: lens 1 are (V1+U2) with the spacing of lens 2, U2=2f2; Lens 2 are (V2+U3) with the spacing of lens 3.

3. imaging analysis: what lens 3 will become in accompanying drawing 3e is the equal-sized upright virtual image of the relative original, and the virtual image is positioned at original place, i.e. L03=V3.According to formula 1., object distance is the picture that the object of two focus length will become to stand upside down and equate at lens the opposing party's two focus length place, so in order to reduce variable, we are positioned at lens 1 imaging at the 2f2 place of lens 2, be U2=2f2=V2, since will 3 one-tenths on lens be the equal-sized upright virtual image of the relative original, so the upright real image of the relative original that is become through lens 2 must be to be in the f3.

4. conclusion: shown in the accompanying drawing 3f, do not have the amphicheirality.

Wherein, design formula:

If U ₁=x (x＞2f ₁) S ₁=S ₄=a

${\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">V</figure-callout>}}_1=\frac{U_1{f}_1}{U_1-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}=\frac{x{f}_1}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}$ $\underset{\&CenterDot;}{\&CenterDot;\&CenterDot;}\frac{S_2}{{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">S</figure-callout>}}_1}=\frac{V_1}{{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">U</figure-callout>}}_1}$ $\stackrel{\&CenterDot;}{\&CenterDot;\&CenterDot;}{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">S</figure-callout>}}_2=\frac{V_1{S}_1}{{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">U</figure-callout>}}_1}=\frac{f_{1}a}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}$ $\underset{\&CenterDot;}{\&CenterDot;\&CenterDot;}\frac{1}{U_3}-\frac{1}{{\mathrm{<figure-callout\; id="3"\; label="V"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">V</figure-callout>}}_3}=\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}$ $\stackrel{\&CenterDot;}{\&CenterDot;\&CenterDot;}\frac{1}{{\mathrm{<figure-callout\; id="3"\; label="V"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">V</figure-callout>}}_3}=\frac{f_1-U_3}{U_3{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}$

$\frac{S_3}{{\mathrm{<figure-callout\; id="4"\; label="S"\; filenames="A20081003732700292.png"\; state="\{\{state\}\}">S</figure-callout>}}_4}=\frac{U_3}{{\mathrm{<figure-callout\; id="3"\; label="V"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">V</figure-callout>}}_3}$ ∵ S again ₂=S ₃ $\stackrel{\&CenterDot;}{\&CenterDot;\&CenterDot;}\frac{\frac{f_{1}a}{x-f_1}}{a}=\frac{f_1-U_3}{U_3{f}_1}{\mathrm{<figure-callout\; id="3"\; label="U"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">U</figure-callout>}}_3\&DoubleRightArrow;{\mathrm{<figure-callout\; id="3"\; label="U"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">U</figure-callout>}}_3=\frac{(x-2f_1)f_1}{x-f_1}$ ${\mathrm{<figure-callout\; id="12"\; label="L"\; filenames="A20081003732700322.png"\; state="\{\{state\}\}">L</figure-callout>}}_{12}=\frac{x{f}_1}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}+2f_2{L}_{23}=\frac{(x-2f_1)f_1}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}+2{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">f</figure-callout>}}_2$

Present embodiment, lens 4 be set to n ∈ { n|n=2x+1, x ∈ N ^*1 above odd number piece biconvex lens imaging design of odd number piece biconvex lens (shown in accompanying drawing 3g)

If: lens 1 are (V1+U2) with the spacing of lens 2, U2=2f2; Lens 2 are (V2+U3+4fz (n-1)) with the spacing of lens 3

Wherein,

F1: one times of focal length of lens 1;

F2: one times of focal length of lens 2;

Fz: one times of focal length of newly-increased lens;

U1: the object distance of lens 1;

V1: the image distance of lens 1;

U2: the object distance of lens 2;

V2: the image distance of lens 2;

U3: the object distance of lens 3;

V3: the image distance of lens 3;

L12: the interval of lens 1 and lens 2;

L23: the interval of lens 2 and lens 3;

L03: the distance apart from lens 3 in kind.

General introduction: adopt at increase biconvex lens number in pairs between the biconvex lens 2 of last scheme and the lens 3 for 1 above odd number piece biconvex lens design.And make lens 2 to become the spacing of real image and newly-increased biconvex lens 11 be 2fz; Between newly-increased biconvex lens 1 (n-1) and the lens 3 is (2fz+U3); Make the spacing of newly-increased biconvex lens 11 and newly-increased biconvex lens 12 ... be 4fz to reaching the spacing of newly-increased biconvex lens 1 (n-2) with newly-increased biconvex lens 1 (n-1).Do not change last conceptual design thought thereby play, the purpose of real image that symmetrical relay len 2 becomes.The focal distance f z of newly-increased biconvex lens can biconvex lens 2 focal length identical.

Wherein, design formula:

If U ₁=x (x＞2f ₁)

${\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">V</figure-callout>}}_1=\frac{U_1{f}_1}{U_1-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}=\frac{x{f}_1}{x-f_1}$ ${\mathrm{<figure-callout\; id="3"\; label="U"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">U</figure-callout>}}_3=\frac{(x-2f_1)f_1}{x-f_1}$ ${\mathrm{<figure-callout\; id="12"\; label="L"\; filenames="A20081003732700322.png"\; state="\{\{state\}\}">L</figure-callout>}}_{12}=\frac{x{f}_1}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}+2f_2{L}_{23}=\frac{(x-2f_1)f_1}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}+2{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">f</figure-callout>}}_2+4f_z(n-1)$

Apparatus of the present invention embodiment 4

At least one group can allow light see through by one and the articles 1 of its focusing and the beam Propagation parts 2 and stealthy district more than 3 parts that are arranged at 1 of the articles of this focusing are constituted.Wherein, the articles 1 of described light focusing adopts a plano-convex lens group, and described beam Propagation parts 2 (being lens 4) are the even numbered blocks biconvex lens.(shown in accompanying drawing 3h)

About lens (4) is even numbered blocks biconvex lens imaging design

Present embodiment, the number that is provided with of lens 4 is 2 biconvex lens

2 biconvex lens imaging designs (shown in accompanying drawing 3i)

Wherein,

F1: one times of focal length of lens 1;

F2: one times of focal length of lens 2;

U1: the distance apart from lens 1 in kind;

U2: lens 1 imaging is apart from the distance of lens 2;

U3: lens 2 imagings are apart from the distance of lens 3;

U4: lens 3 imagings are apart from the distance of lens 4;

V1: the image distance of lens 1;

V2: the image distance of lens 2;

V3: the image distance of lens 3;

V4: the image distance of lens 4.

1. general introduction: light that object reflects is through 1 one-tenths real image that stands upside down and dwindle of lens, image position in 2 times of focal lengths of lens 2,1 times out-of-focus, this real image is through 2 one-tenth upright real images of the relative original of lens.As axis of symmetry, the lens position on the left side is symmetric to the right with the position of this upright real image, places lens, light will become the relative original to equate and upright real image on the right of lens 4.

2. the position between lens concerns: lens 1 are (V1+U2) with the spacing of lens 2; Lens 2 are (V2+U3) with the spacing of lens 3; Lens 3 are (V3+U4) with the spacing of lens 4, and (U1, U2, U3, U4, V1, V2, V3, V4 all greater than 1 times of focal length of lens) separately, and wherein, lens 1 are identical with lens 4, and lens 2 are identical with lens 3.

3. imaging analysis: lens 4 will become in accompanying drawing 4b is relative original equal and opposite in direction, upright real image, i.e. U1=V4.According to formula 1., derive: U4=V1; Because identical between the real image between the lens 1 and 2 and lens 3 and 4, lens 2 and 3 are identical lens in addition, thus U2=V3, i.e. V2=U3, whole device is about red dotted line symmetry.

4. conclusion: shown in the accompanying drawing 3i, 2 lens have the amphicheirality.

Wherein, design formula:

If U ₁=x (x＜f ₁) S ₁=S ₅=a

${\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">V</figure-callout>}}_1=\frac{f_1{U}_1}{U_1-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}=\frac{f_{1}x}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}$ ∵V ₁＝U ₄ $\underset{\&CenterDot;}{\&CenterDot;\&CenterDot;}{\mathrm{<figure-callout\; id="4"\; label="U"\; filenames="A20081003732700292.png"\; state="\{\{state\}\}">U</figure-callout>}}_4=\frac{f_{1}x}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}$ If U ₂, V ₂, U ₃, V ₃=2f ₂

${\mathrm{<figure-callout\; id="12"\; label="L"\; filenames="A20081003732700322.png"\; state="\{\{state\}\}">L</figure-callout>}}_{12}=\frac{f_{1}x}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}+2f_2$ L ₂₃＝4f ₂ $L_{34}=\frac{f_{1}x}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}+2{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">f</figure-callout>}}_2$

Present embodiment, { n|n= 2x+ 2,2 above even numbered blocks biconvex lens imagings of x ∈ N*} even numbered blocks biconvex lens design (shown in accompanying drawing 3j) to the n ∈ that is set to of lens 4

Between 2 biconvex lens 2 and biconvex lens 3, increase the biconvex lens number in pairs.And make lens 2 to become the spacing of real image and newly-increased biconvex lens 11 be 2fz; Between newly-increased biconvex lens 1 (n-2) and the lens 3 is (2fz+U3); Make the spacing of newly-increased biconvex lens 11 and newly-increased biconvex lens 12 ... be 4fz to reaching the spacing of newly-increased biconvex lens 1 (n-3) with newly-increased biconvex lens 1 (n-2).Do not change last conceptual design thought thereby play, the purpose of real image that symmetrical relay len 2 becomes.The focal distance f z of newly-increased biconvex lens is can biconvex lens 2 identical with the focal length of biconvex lens 3.

Even numbered blocks biconvex lens imaging analysis:

Wherein,

F1: one times of focal length of lens 1;

F2: one times of focal length of lens 2;

Fz: one times of focal length of newly-increased lens;

U1: the distance apart from lens 1 in kind;

U2: lens 1 imaging is apart from the distance of lens 2;

U3: lens 2 imagings are apart from the distance of lens 3;

U4: lens 3 imagings are apart from the distance of lens 4;

V1: the image distance of lens 1;

V2: the image distance of lens 2;

V3: the image distance of lens 3;

V4: the image distance of lens 4.

Wherein, design formula:

If U ₁=x (x＞f ₁)

${\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">V</figure-callout>}}_1=\frac{f_1{U}_1}{U_1-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}=\frac{f_{1}x}{x-f_1}$ ${\mathrm{<figure-callout\; id="4"\; label="U"\; filenames="A20081003732700292.png"\; state="\{\{state\}\}">U</figure-callout>}}_4=\frac{f_{1}x}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}$

${\mathrm{<figure-callout\; id="12"\; label="L"\; filenames="A20081003732700322.png"\; state="\{\{state\}\}">L</figure-callout>}}_{12}=\frac{f_{1}x}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}+2f_2$ L ₂₃＝4f ₂+4f _z(n-2) $L_{34}=\frac{f_{1}x}{x-{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20081003732700283.png,A20081003732700292.png"\; state="\{\{state\}\}">f</figure-callout>}}_1}+2{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="A20081003732700283.png,A20081003732700293.png"\; state="\{\{state\}\}">f</figure-callout>}}_2$

Another specific embodiment of apparatus of the present invention,

When non-parallel light is light source, select 4,6,8 even numbered blocks lens for use.

Described lens are respectively:

Plano-convex lens: diameter=80mm focal length=150mm quantity 2;

Crescent moon is bent convex lens: diameter=110mm focal length=230mm quantity 2;

Biconvex lens: diameter=25mm focal length=25mm quantity 1;

Diameter=16mm focal length=16mm quantity 1;

Diameter=40mm focal length=100mm quantity 1

Experimental data

1 lens devices experimental data

Unit (mm)	Φ 1	f 1	n 1	Φ 2	f 2	n 2	u 1	L 1	L 2
										Experiment 1	80	150	2	25	25	1	5000	165	170
Experiment 2	80	150	2	16	16	1	5000	155	160
										Experiment 3	80	150	2	40	100	1	5000	160	160
Experiment 4	80	150	2	40	100	1	5000	355	346
										Experiment 5	110	230	2	40	100	1	5000	441	421

Summary is used in expansion about apparatus of the present invention

Space industry and military armor facing field

This device is on the porthole of aerospace craft, and the perhaps utilization on the hagioscope of armor facing car not only can reach existing high strength glass visible observation effect to external world, and has more the effect of security protection. To keeping out extraneous high-speed impact, such as objects such as bullet, space debris good protection effect is arranged.

Military field: a kind of anti-terrorism Detecting Robot (device) that possesses hidden function, its apparatus structure is: according to the by formula required configuration that comprises selection form of lens and quantity and beam Propagation parts of calculation Design device of height (or volume) of robot, robot is arranged on the stealth district of device. According to principle of device of the present invention, under 10 meters left and right sides conditions, in the first visual angle situation, the witness can only see transparent " object " and the background thereof that moves, and can't find by the robot of stealth.

Building field: the wall that uses this technology stealthy needn't see, pillar, roof, or even low rise buildings. Make up take certain area as unit, just can stealthy bulk area.

Space industry: passenger plane and manned spacecraft all need to be windowed at side of a ship body. And the cost of this glass pane is very expensive, and makes the technology of this kind glass, is still monopolized by minority enterprise. Application technology can reduce the usage degree of this glass greatly. Originally must open a very large hole at side of a ship body, the required size of biconvex lens diameter in the middle of need only leaving now. Not only save cost, also increase the security of cabin body.

World of art: be raw material with high-grade mineral crystal or diamond, use this technology to make the stealthy volume cross section stealthy ring consistent with the finger cross section. Scientific value can be risen to artistic value.

In sum, by core of the present invention: at least one group can be made light see through and with the object of its focusing be arranged at the device that several parts of beam Propagation parts and stealthy district between the object of this focusing consist of, had compared with the prior art: utilize the geometric optics principle to reach the effect of the optical invisible of visible light by a pair of; Do not need the extra power supply during the stealthy state of holdout device; The outer exposed part of device is less; Especially, have good concealment than the optical physics hidden apparatus, simple in structure, easily make, but cost is low and the characteristics of extensive use.

Claims (7)

1. the hidden apparatus based on geometric optical theory is characterized in that, at least one group can allow light see through by one and the articles (1) of its focusing and beam Propagation parts (2) and the stealthy district (3) that is arranged between this articles (1) are formed.

2. a kind of hidden apparatus based on geometric optical theory as claimed in claim 1 is characterized in that, described articles (1) is the convex lens of a plating anti-reflection film, perhaps is the positive balsaming lens of achromatism of a plating anti-reflection film, perhaps is a zone plate.

3. as claim 1,2 described a kind of hidden apparatus based on geometric optical theory, it is characterized in that described beam Propagation parts (2) are an optical fiber, perhaps is a silverskin reflection tube, perhaps is lens (4).

4. a kind of hidden apparatus based on geometric optical theory as claimed in claim 3 is characterized in that described lens (4) are a biconvex lens.

5. the design of a kind of hidden apparatus based on geometric optical theory as claimed in claim 1 is characterized in that,

Stealthy volume calculation formula: V=S1*L1-2/3*S1*f-S2* (L1-2f)

Wherein, V: by stealthy volume;

S1: both sides can focus on the cross-sectional area of articles (1);

L1: both sides can focus on the spacing of articles (1);

F: both sides can focus on the focal length of articles (1);

S2: the cross-sectional area of beam Propagation parts (2);

Described lens (4) are pressed directional light design formula: Ra/fa=Rb/2fb

Wherein, Ra: the radius of lens a;

Rb: the radius of lens b;

Fa: one times of focal length of lens a;

Fb: one times of focal length of lens b.

6. the design of a kind of hidden apparatus based on geometric optical theory as claimed in claim 5 is characterized in that,

Wherein establish: lens 1 are (V1+U2+4fz (n-1)) with the spacing of lens 2, U2＜f2,

Lens 2 are (U3-V2) with the spacing of lens 3,

Then described lens (4) be provided with n ∈ n|n=2x+1, its design formula of x ∈ N*} odd number piece biconvex lens:

If U ₁=x S ₄=S ₁=a V ₃=y (x, y all＞f ₁)

$V_1=\frac{f_1{U}_1}{U_1-f_1}=\frac{f_{1x}}{x-f_1}$ $U_3=\frac{f_{1y}}{y-f_1}$ $U_2=\frac{x-y}{x-f_1}{f}_2$ $V_2=\frac{x-y}{y-f_1}{f}_2$

$L_{12}=\frac{f_{1x}+f_2(x-y)}{x-f_1}+4f_z(n-1)$ $L_{23}=U_3-V_2=\frac{f_{1y}-f_2(x-y)}{y-f_1}$

If must have the amphicheirality, x and y still satisfy: $\frac{f_{1x}+f_2(x-y)}{x-f_1}=\frac{f_{1y}-f_2(x-y)}{y-f_1}$

Wherein,

F1: one times of focal length (f1=f3) of lens 1;

F2: one times of focal length of lens 2;

Fz: one times of focal length of newly-increased lens;

U1: the object distance of lens 1;

V1: the image distance of lens 1;

U2: the object distance of lens 2;

V2: the image distance of lens 2;

U3: the object distance of lens 3;

V3: the image distance of lens 3;

Described lens (4) are provided with

Wherein establish: lens 1 are (V1+U2) with the spacing of lens 2, U2＜f2,

Lens 2 are (U3-V2) with the spacing of lens 3,

And odd number piece biconvex lens number is 1, then its design formula:

If U ₁=x S ₄=S ₁=a V ₃=y (x, y all＞-f ₁)

$V_1=\frac{f_1{U}_1}{U_1-f_1}=\frac{f_{1x}}{x-f_1}$ $S_2=\frac{V_1}{U_1}$ $S_1=\frac{f_{1a}}{x-f_1}$ In like manner: $S_3=\frac{f_{1a}}{y-f_1}$ $U_3=\frac{f_{1y}}{y-f_1}$ $\underset{.}{..}\frac{S_2}{S_3}=\frac{U_2}{V_2}$ $\stackrel{.}{..}\frac{y-f_1}{{x-f}_1}=\frac{U_2}{V_2}$

If U ₂=(y-f ₁) k V ₂=(x-f ₁) k

$\underset{.}{..}\frac{1}{f_2}=\frac{1}{U_2}-\frac{1}{V_2}$ $\stackrel{.}{..}\frac{1}{f_2}=\frac{1}{k}(\frac{1}{y-f_1}-\frac{1}{x-f_1})$ $\stackrel{.}{..}k=\frac{x-y}{(x-f_1)(y-f_1)}{f}_2$ $\stackrel{.}{..}{U}_2=\frac{x-y}{x-f_1}{f}_2$ $V_2=\frac{x-y}{y-f_1}{f}_2$

$L_{12}=\frac{f_{1x}+f_2(x-y)}{x-f_1}$ $L_{23}=U_3-V_2=\frac{f_{1y}-f_2(x-y)}{y-f_1}$

If must have the amphicheirality, then $L_{12}=L_{23}\&DoubleRightArrow;x$ Should satisfy with y: $\frac{f_{1x}+f_2(x-y)}{x-f_1}=\frac{f_{1y}-f_2(x-y)}{y-f_1}$

Wherein,

F1: one times of focal length (f1=f3) of lens 1;

F2: one times of focal length of lens 2;

U1: the object distance of lens 1;

V1: the image distance of lens 1;

U2: the object distance of lens 2;

V2: the image distance of lens 2;

U3: the object distance of lens 3;

V3: the image distance of lens 3;

L12: the spacing of lens 1 and lens 2;

L23: the spacing of lens 2 and lens 3;

Described lens (4) are provided with

Wherein establish: lens 1 are (V1+U2) with the spacing of lens 2, U2=2f2,

Lens 2 are (V2+U3+4fz (n-1)) with the spacing of lens 3,

Then n ∈ n | n=2x+1, x ∈ N ^*Its design formula of odd number piece biconvex lens:

If U ₁=x (x＞-2f ₁)

$V_1=\frac{U_1{f}_1}{U_1-f_1}=\frac{x{f}_1}{x-f_1}$ $U_3=\frac{(x-2f_1)f_1}{x-f_1}$ $L_{12}=\frac{x{f}_1}{x-f_1}+2f_2$ $L_{23}=\frac{(x-2f_1)f_1}{x-f_1}+2f_2+4f_z(n-1)$

Wherein,

F1: one times of focal length of lens 1;

F2: one times of focal length of lens 2;

Fz: one times of focal length of newly-increased lens;

U1: the object distance of lens 1;

V1: the image distance of lens 1;

U2: the object distance of lens 2;

V2: the image distance of lens 2;

U3: the object distance of lens 3;

V3: the image distance of lens 3;

L12: the spacing of lens 1 and lens 2;

L23: the spacing of lens 2 and lens 3;

L03: the distance apart from lens 3 in kind

Wherein establish: lens 1 are (V1+U2) with the spacing of lens 2, U2=2f2,

Lens 2 are (V2+U3) with the spacing of lens 3,

And the odd number piece biconvex lens number of described lens (4) is 1 o'clock, then its design formula:

If U ₁=x (x＞2f ₁) S ₁=S ₄=a

$V_1=\frac{U_1{f}_1}{U_1-f_1}=\frac{x{f}_1}{x-f_1}$ $\underset{.}{..}\frac{S_2}{S_1}=\frac{V_1}{U_1}$ $\stackrel{.}{..}{S}_2=\frac{V_1{S}_1}{U_1}=\frac{f_{1a}}{x-f_1}$ $\underset{.}{..}\frac{1}{U_3}-\frac{1}{V_3}=\frac{1}{f_1}$ $\stackrel{.}{..}\frac{1}{V_3}=\frac{f_1-U_3}{U_3{f}_1}$

$\frac{S_3}{S_4}=\frac{U_3}{V_3}$ ∵ S again ₂=S ₃ $\stackrel{.}{..}\frac{\frac{f_{1a}}{x-f_1}}{a}=\frac{f_1-U_3}{U_3{f}_1}{U}_3\&DoubleRightArrow;U_3=\frac{(x-2f_1)f_1}{x-f_1}$ $L_{12}=\frac{x{f}_1}{x-f_1}+2f_2$ $L_{23}=\frac{(x-2f_1)f_1}{x-f_1}+2f_2$

Wherein,

F1: one times of focal length of lens 1;

F2: one times of focal length of lens 2;

Fz: one times of focal length of newly-increased lens;

U1: the object distance of lens 1;

V1: the image distance of lens 1;

U2: the object distance of lens 2;

V2: the image distance of lens 2;

U3: the object distance of lens 3;

V3: the image distance of lens 3;

L12: the spacing of lens 1 and lens 2;

L23: the spacing of lens 2 and lens 3;

L03: the distance apart from lens 3 in kind.

7. the design of a kind of hidden apparatus based on geometric optical theory as claimed in claim 5 is characterized in that,

Wherein establish: lens 1 are (V1+U2) with the spacing of lens 2,

Lens 2 are (V2+U3+4fz (n-2)) with the spacing of lens 3,

Lens 3 are (V3+U4) with the spacing of lens 4, and U1, and U2, U3, U4, V1, V2, V3, V4 be all greater than one times of focal length of lens separately,

The n ∈ of then described lens (4) n|n=2x+2, and x ∈ N*} even numbered blocks biconvex lens, its design formula:

If U ₁=x (x＞-f ₁)

$V_1=\frac{f_1{U}_1}{U_1-f_1}=\frac{f_{1x}}{x-f_1}$ $U_4=\frac{f_{1x}}{x-f_1}$

$L_{12}=\frac{f_{1x}}{x-f_1}+2f_2$ L ₂₃＝4f ₂+4f _z(n-2) $L_{34}=\frac{f_{1x}}{x-f_1}+2f_2$

Wherein,

F1: one times of focal length of lens 1;

F2: one times of focal length of lens 2;

Fz: one times of focal length of newly-increased lens;

U1: the distance apart from lens 1 in kind;

U2: lens 1 imaging is apart from the distance of lens 2;

U3: lens 2 imagings are apart from the distance of lens 3;

U4: lens 3 imagings are apart from the distance of lens 4;

V1: the image distance of lens 1;

V2: the image distance of lens 2;

V3: the image distance of lens 3;

V4: the image distance of lens 4;

Wherein establish: lens 1 are (V1+U2) with the spacing of lens 2,

Lens 2 are (V2+U3) with the spacing of lens 3,

Lens 3 are (V3+U4) with the spacing of lens 4, and U1, and U2, U3, U4, V1, V2, V3, V4 be all greater than one times of focal length of lens separately,

And the even numbered blocks biconvex lens number of described lens (4) is 2, then its design formula:

If U ₁=x (x＞-f ₁) S ₁=S ₅=a

$V_1=\frac{f_1{U}_1}{U_1-f_1}=\frac{f_{1x}}{x-f_1}$ ∵V ₁＝U ₄ $\underset{.}{..}{U}_4=\frac{f_{1x}}{x-f_1}$ If U ₂, V ₂, U ₃, V ₃=2f ₂

$L_{12}=\frac{f_{1x}}{x-f_1}+2f_2$ L ₂₃＝4f ₂ $L_{34}=\frac{f_{1x}}{x-f_1}+2f_2$

Wherein establish: the U1=x (S1=S5=a of x＞f1)

V1＝f1U1/U1-f1＝f1x/x-f1

∵V1＝U4 ∴U4＝f1x/x-f1

If U2, V2, U3, V3=2f2

L12＝(f1x/x-f1)+2f2 L23＝4f2

L34＝(f1x/x-f1)+2f2

Wherein,

F1: one times of focal length of lens 1;

F2: one times of focal length of lens 2;

U1: the distance apart from lens 1 in kind;

U2: lens 1 imaging is apart from the distance of lens 2;

U3: lens 2 imagings are apart from the distance of lens 3;

U4: lens 3 imagings are apart from the distance of lens 4;

V1: the image distance of lens 1;

V2: the image distance of lens 2;

V3: the image distance of lens 3;

V4: the image distance of lens 4.

Images