DESCRIPTION OF THE PREFERRED
Membrane material is transparent, and is designed to an inner member of system, and it is a part therein.Film comprises one group of indentation or discontinuous shape of being filled with reflecting material.The cross section of indentation presents can be with triangle or other polyhedron shape of various patterns arrangements.Indentation can replace to a succession of discontinuous object that resembles cone, cone or the arbitrary polyhedron, can arrange with various patterns equally.The discontinuity surface of indentation or object can be the plane, concave surface, convex surface or pitted, can control the light of all face reflections like this.The preferred material of filling indentation is to resemble aluminium or the silver-colored material that has high reflectance like this, but can be complexing agent, composite or multiple material with different refractivity or volume reflection.Reflecting material is embedded among the transparent material, and the bottom of every kind of shape and transparent material are parallel substantially like this, overlaps with transparent material or slightly recessed.Indentation or the parallel repeated arrangement of discontinuous object, transmembrane zone at certain intervals.Before repeat pattern indentation or discontinuous object can be with different shape, highly, angle or be spaced.
In Fig. 3, represent transparent material, 15 expression reflection indentation or objects, 12 expression backlight assemblies, the remainder of 16 expression nothing emission display systems and the direction of watching demonstration with 14.Order:
The half width of 17=r=groove or object bottom
The bottom of 2r=groove or object
The multiple of f=bottom portion of groove half width
Interval between the 18=fr=groove
19=Th=film thickness (according to the height of groove or object, by the character decision of transparent material)
The multiple of K=bottom portion of groove half width
The height of 20=Kr=groove or object
The groove quantity of each pixel of 21=M=(image component) is defined as the minimum controllable zone of demonstration here
Also order
R
M2=reflecting material is to normal reflection of incident light rate
The whole invention of 22 expressions
Comprise that by being used in combination suitably (1) setting the material of film and (2) select to have either different reflectivity, refractive index materials, composite or both combinations and reach similar minute surface or concentrate effect.Light orientation/concentrating structure and/or micro-structural include, but are not limited to zigzag (intersect or do not intersect), taper or other conic section, resemble the many side structures (rule or irregular) pyramid or the tetrahedron.The general periodic variation of structure that all sizes are identical or different, the reflectivity of film, transmissivity and absorptivity have different values.This can obtain high reflectance and low transmissivity by film in a direction, obtains high-transmission rate and antiradar reflectivity in another direction.
R
1The reflectivity of=one side
T
1The transmissivity of=one side
A
1The absorptivity of=one side
R
2The reflectivity of=opposite side
T
2The transmissivity of=opposite side
A
2The absorptivity of=opposite side
According to the conservation of energy: R
1+ T
1+ A
1=1 and R
2+ T
2+ A
2=1.
In the multiple reflection body of prior art, R=R
1=R
2T=T
1=T
2And A=A
1=A
2Can reach a conclusion thus, in existing design when A=0, R+T=1.Even require to overcome the restriction of multiple reflection body and the multiple reflection body of proposition must guide or directional light in prior art, not total transmissivity or total reflection but demonstrate, thus can determine any possible gain, and gain is unconspicuous.
In this technology, bigger the separating of reflected value of the reflected value of film one side and opposite side, the transmission value of a side and bigger the separating of the transmission value of opposite side.The film of this new proposition allows R
1≠ R
2T
1≠ T
2And A
1≠ A
2To show T below
1, R
1, A
1And A
2Be worth little particular.Therefore can draw R
1+ T
2>1.This film that proposes has increased transmission reflection (trans-flecting) effect.On theoretical boundary, for this nothing emission pattern of film, T
1=R
2=A
1=A
2=0.R so
1+ T
2=1.
First embodiment of film relates to the use in the orientation of the light of not considering the transmission scattering, particularly in directed or the solar collector of collection radiant light or the use in any equipment, as shown in Figure 4.In this figure, the light that the sun 23 sends enters transparent material with light ray 10A, directly is transmitted to absorbing material 24.Light ray 10B passes transparent material 14, and part is by absorbing material 24 reflections.Light ray 10C passes transparent material 14, is redirected to absorbing material 24 by catoptric arrangement 15, and part is by absorbing material 24 reflections.Be complementary for other element of the system of a part wherein by suitable selective refraction rate and membrane material, membrane material has high optical transmittance to visible light, ultraviolet light and/or the near infrared light between about 300-2500 nanometer, to ultraviolet light is stable, can not see through moisture, non-hygroscopic, anti scuffing and is easy to keep clean.Adhesive has high optical transmittance to the light between about 300-2500 nanometer, and is stable to ultraviolet light.Be in the first embodiment for transmissivity and reflectivity with design maximum.So will gather the daylight of maximum and remain on film be wherein a part particular device in.Therefore, embodiment makes R hereto
M2=1.00; A kind of complete reflecting material.Make f=0.1, the practical limit that indentation is made.For r and the enough big value of f selection, avoid diffraction effect and interference effect.For example, select r=200 μ, make that the distance between the adjacent indentations bottom is 20 μ, fully greater than the long wavelength of visible light.As long as for having used complete reflecting material, the multipath reflection during the transmission is with regard to inessential solar collector, R
1=2/ (2+f)=0.952, T
2=1.000.So R
1+ T
2=1.952, near theoretical boundary 2.000.Therefore, in fact will collect the luminous energy that all enter system.Second embodiment of film relates to and is used for a kind of nothing emission display system, for example liquid crystal display, or the equipment of other directional light in order to produce image.The embodiment of this film can be inserted between backlight assembly and the display system remainder, can be an assembly of backlight assembly, perhaps can be attached on the assembly of remainder of demonstration.Preferred in this case artificial light sources comprises the device of a collimated light, thereby most of light are vertically penetrated on film.High transmission one side of the film that is proposed is to back light system, and high reflectance one side is to the beholder.Film covers whole viewing areas.Indentation or object can with respect to show the edge, from parallel to the align at random angles that tilts.
Use nothing emission display system of the present invention by forming of in Fig. 5, illustrating.In this accompanying drawing, surround lighting 10 passes different layers, 6 polariscopes, 7 glass plates (can comprise color filter mirror, common electrode, TFT matrix or other assembly) and 8 liquid crystal suspended substances, change direction by reflecting element 22 of the present invention, to the different layers that returns by 6 to 8, and the artificial light ray 13 that is produced by backlight assembly 12 simultaneously passes translucent element 22 of the present invention, translucent element can be attached to close on, resemble on the such element of backlight assembly 12, or as one independently layer be installed in the display system.
If
W
T=display width
The indentation quantity of each pixel of m=(image component) is defined as the minimum controllable zone of demonstration here.
F
WThe display format of=horizontal direction (quantity of different elements, wherein each element has a red, green, blue pixel)
So for colour liquid crystal display device, r=W
T/ [3F
WM (2+f)].For method for designing is described, make W
T=246mm and F
W=800 represent the representative value of colour liquid crystal display device design in 1996/97 year.In addition, make m=3, eliminated the needs that film alignd with display pixel during display unit was handled.In addition, can increase or reduce m on demand, to eliminate significantly, may be the light skewness that produces by film, for example striped.
The design that is used for second embodiment for showing makes f=0.5.It is minimum that this changes direction of light, kept its original orientation of transmitted light.F value hereto can unreflecting transmission from the directional light 20% of back light system, and 40% can be because reflection indentation or object change first power transmission backward, and 40% can be because reflection indentation or object change quadratic power transmission backward.In this example, can use equation r=W
T/ [3F
WM (2+f)] to calculate r be 13.7 μ, then fr (interval between the indentation) is 6.9 μ at interval.If R
M2Known (standard reflectivity of material) can calculate reflectivity R
1With transmissivity T
2Note two design example:
1. make R
M2=1, R then
1=2/ (2+f)=0.8.T
2=1.0, obtain R
1+ T
2=1.8.
2. make R
M2=0.86, R so
1=2R
M2/ (2+f)=0.8.T
2=0.840, obtain R
1+ T
2=1.528.
Two kinds of designs show by using the multiple reflection body technique to replace existing Transflective body technique and can be greatly improved.
Resemble used hereinly, the multiple reflection body is the Transflective body, is can transmission and catoptrical equipment.
Fig. 6 has shown a kind of embodiment.Represent transparent material (main body of element) with 31,32 expression reflection/refraction shapes, 33 represent reflecting materials, and (wherein do not have filling, using gases, vacuum or change refractive index generate structure.), 34 expressions are attached to the collimating element on the multiple reflection body member.(not show) enters element to light ray 36 from the transmission potential source, and what do not change direction passes collimating light pipe 34, passes element body 31 under the situation that does not shine any shaped structure 32, does not change the reflecting surface that leaves element of direction.(not demonstration) enters element to light ray 37 from the transmission potential source with the incidence angle greater than 10 degree, and it is less than 10 degree that collimated light pipe 34 changes directions.Light ray 37 enters element body 31, does not change passing of direction.
Fig. 7 has described the cross section of multiple reflection body member, wherein the edge of 41 expression elements.Structure 43 stretches into the certain percentage of the total component thickness of element.The angle that makes the summit (tip) of structure 43 is 4 degree.In addition, the summit that makes structure 43 is towards a light source (not showing), and the bottom faces of structure 43 is to another light source (not showing) simultaneously.Light ray 44 enters element perpendicular to the plane of element, passes element under the situation that does not shine any shaped structure 43, does not change the element that leaves of direction.Light ray 45 enters element perpendicular to the plane of element, shines the mid point of structure 43, by the change direction of minimum degree (with respect to element plane vertical line 4 degree), can not shine adjacent structure 43 like this and leaves element.Light ray 46 enters element perpendicular to the plane of element, near summit (tip), shine structure 43, by the change direction of minimum degree (with respect to element plane vertical line 4 degree), near structural base, shine adjacent structure (structure height 16.6%) like this, by the change direction (as above) of minimum degree, light ray 46 total direction when leaving element changes deviation element plane vertical line 8 degree so once more.Light ray 47 enters element with the angle greater than element plane vertical line 10 degree, shines structure 43 on mid point, by the change direction of minimum degree (with respect to element plane vertical line 4 degree).Because light ray 47 incident angles increase, direction took place repeatedly before light ray 47 leaves element change.In this example, light ray 47 leaves element needs seven directions to change---and accumulative total changes direction 28 degree.Light ray 48 is reflected with the angle that equals incidence angle by structure 43.Light ray 49 enters element with the angle excessive with respect to the plane vertical line, shines structure 43 near summit (tip), because the direction of accumulative total changes, light ray 49 can not leave the opposing face of element.
Fig. 7 is with 14.3 depth-width ratio configuration structure 43, is spaced apart 25% of bottom width between the structure 43, and even structure is spaced across element body 42.This element reaches 94% the light ray transmissivity that enters element perpendicular to the plane from the one side on the most close structure 43 summits (tip).The other benefit that above-described element provides is the light that reflection 76% shines element the other way around.In this example, the light 20% that enters from transmission plane does not change the element that passes of direction, and 40% passes element with first power to changing (with respect to element plane vertical line 4 degree), and 40% light has twice direction to change (with respect to element plane vertical line 8 degree).This example R+T is 1.70.
The combination of above-described depth-width ratio and spacing structure is for the effect of arrangements of components is described, is not in order to limit.
Another embodiment of the invention relates to the use in after transmission orientation or the focused light, particularly is used among the construction material, wherein uses sunshine to illuminate interior zone or strengthens artificial light.In this embodiment, indentation or object can change angle, and the bottom of indentation or object is not parallel with the border of transparent material or do not overlap like this.This embodiment allows light to be directed to transparent material with given angle, and is irrelevant with the angle of light source.
The present invention can be expressed as a Transflective body, be useful on the device of reflection from the light of first direction reflected illumination on it, have transmission from the device of the light of first direction rightabout irradiation, wherein Fan She light with respect to from the light of the percentage of first party light always and transmission with respect to the percentage of the light that comes the other way around and greater than a hundred per cent.
The present invention also can explain one can be at the transparent material of the first and second direction transmitted lights, a first surface is arranged, first surface is useful on the reflecting part but is not the device that all shines the light of first surface from first direction, and one or more structures relevant with arrangement of reflectors are arranged.This structure has the sidewall that stretches out from first surface, the angle of sidewall enough reflects passes first surface shines structure from second direction light, light from second direction partly passes first surface like this, wherein Fan She light with respect to from the light of the percentage of first party light always and transmission with respect to from the percentage of the light quantity of second direction and greater than absolutely.
The multiple reflection body member is independent of all particular systems, includes but the typical case is as the several elements among the system one.The multiple reflection body member provides energy reflection best on the direction, and best energy transmission is provided simultaneously in the opposite direction.This is by using embedding, relief or finishing by the high depth-width ratio structure that other method forms in element body.By increasing reflection/refraction structure greatly at the surface area of a direction (summit of structure) with respect to structural base, the amount of the energy that can reflect a direction can be separated with the amount of the energy of rightabout transmission.
The multiple reflection body member can dispose with other element, to produce other effect.In preferred embodiments, collimating element can combine with the multiple reflection body, forms a discrete component, be attached on the multiple reflection body, or incorporate among another assembly of multiple reflection system that body depends on, collimating element is near the transmission plane of multiple reflection body member, between element and transmitted light source like this.Collimating element is received in the incident energy ripple that distributes in the wide range, can change direction by ripple, makes angle less than some special angle from the element surface normal measure.The use of collimating element has guaranteed that in fact all enter the energy limited of multiple reflection body member in the arc of about 10 degree of element plane vertical line from transmission plane.Limit the performance that transmission potential will improve the multiple reflection body member by this way, but be the necessary condition that the multiple reflection body member produces beneficial effect.
The decisive factor of configuration element is the material that depth-width ratio, the interval between the structure and the structure element of reflection/refraction shaped structure uses.These factors have determined that (1) energy enters the incidence angle that element (transmission) is allowed from a direction, (2) energy is from the ratio of this direction transmission, (3) by the ratio of the energy of element reverse side reflection, (4) energy distributions that penetrates from element, the energy loss percentage of (5) absorbed inside or scattering.The depth-width ratio of reflection/refraction shape (high and the end ratio) has determined transmission potential to enter the special angle of element and transmission potential from the dependency relation between the angle of element ejaculation.Interval determination between the shaped structure by the ratio (from reflecting surface) of the energy of element reflects and the distribution (from transmission plane) of transmission potential.By increasing the interval between the shaped structure,, reduced from rightabout energy reflection simultaneously than the energy change direction from transmission plane of small scale.Otherwise by reducing the interval between the shaped structure, the transmission potential of larger proportion will change direction, and will the reflecting from rightabout transmission potential of larger proportion.Universal relation between the interval between reflection/refraction structure height and the depth-width ratio at the end and the structure has been described in the example below.
Example 1: single structure, cross section are triangles, expand to another side along the total length of element from one side.The structure above the repeated arrangement uniformly-spaced, the one side of whole like this element body is covered by capable bottom of the triangle that replaces and the interval between them.If the application-specific demand for element need be from the approximately reflection 66.6% of energy of one side (reflecting surface), the transmission potential from opposing face is limited in about 5 ° of ejaculations simultaneously, and depth-width ratio was necessary for minimum of a value 11.5: 1 so.Interval between the shaped structure approximately is half of shaped structure bottom size in this example.In this example, be approximately 1.66 (R+T=1.66) with R with addition with T from the transmission potential that comes in handy of opposing face from the reflected energy that comes in handy of one side.This energy 66.6% that can redescribe to enter element from reflecting surface is reflected, and the energy 100% that enters element from transmission plane is by transmission (R=66.6%, T=100%, thereby R+T=166%).
Example 2: suppose the identical of shaped structure and example 1, application-specific demand needs the amount maximum of transmission potential, and is irrelevant with all specific angles of emergence.Also suppose to be corrected to without exception perpendicular within about 10 ° of the element plane from the energy that transmission plane enters element.
In this used, requirement was about 80% a energy of a direction of reflection (reflecting surface), transmission rightabout (transmission plane) greater than 95% energy.Suppose that shaped structure has used complete reflecting material, depth-width ratio is that 15: 1 element transmissivity is approximately 96.8% so.Interval between the shaped structure is approximately 1/4th of shaped structure size.In this example, from the reflected energy that comes in handy of one side and be approximately 1.77 (R+T=1.77) from the transmission potential that comes in handy of opposing face with addition.
In addition, can dispose element with the clearly distribution of control reflection and transmission potential.For instance, this configuration can be used for display application and improves viewing angle.
Near the light ray that shines the triangular structure row summit have possibility leave element before the direction of maximum quantity change.By using basic geometry and to the basic understanding of geometric optics, one can be calculated the width that needs between what kind of depth-width ratio and the structure the skilled people in this area, direction is changed preferably be no more than twice.Can use derive relation between the different parameters of the geometrical curve in light ray path, comprise the constraints of system.The height of structure is determined that by Several Factors one of them is the thickness of transparent material.If application-specific needs transmission to pass the light of Transflective body within vertical 10 degree, supposed height then, can draw so or calculate drift angle.Drift angle and highly determined depth-width ratio, thus determine the width of structural base.
Element should not surpass 100 mil thick in the preferred embodiment of not having the emission demonstration.The transmissive system of element body is greater than 97%.The summit of each formation (tip) penetrates the percentage of element body gross thickness between 10%-100%.Each shape has a fixedly drift angle between 2.6 °-9.5 °, and the ratio at the height and the end is 6: 1-22: between 1.In another embodiment, shape has a fixedly drift angle between 3.0 °-7.0 °, and the ratio at the height and the end is 8: 1-18: between 1.In every kind of embodiment, high ratio the end of with can hang down by 4: 1.This wall that makes structure with respect to the angle at the end about 83 spend less than 90 degree between.The end of shape and the plane parallel of element, the bottom width degree is (μ=micron) between 2.0 μ-200.0 μ.In another embodiment, the bottom width degree can be between 2.0 μ-50.0 μ.Tube shape does not form by packing material or by optical treatment, and the end of each structure must be reflected.This can handle, handle by deposition/photoresist by filling, or other method as coating is finished.The capable structure of triangle with between each triangular apex between the isosceles triangle base adjacent of the fixed intervals between 3.0 μ-300.0 μ with each the fixed intervals repeated arrangement between 1.0 μ-100.0 μ.In another embodiment, the interval between the summit can be between 3.0 μ-70.0 μ, and the interval between the base can be between 1.0 μ-20.0 μ.In preferred embodiments, collimating element is attached near on the element of multiple reflection body member transmission plane.The size of Miao Shuing should not be construed to boundary in preferred embodiments, because other application may need or allow to change according to top specification.
In preferred embodiments, the cross section of single shape is a triangle, expand to another side from one side of element, form a single file, be positioned among the transparent material (element body) and the coincidence or slightly more recessed parallel of leg-of-mutton like this base with a surface plane (reflecting surface) of element body.In preferred embodiments, the capable repetition parallel in the whole zone of element of triangle is also uniformly-spaced arranged, and forms shape and ribbon pattern at interval.In another embodiment, leg-of-mutton row can replace to discontinuous object, and for example pyramid, cone or arbitrary polyhedron equally can be with various arranged in patterns to obtain specific effect.In another embodiment, aforesaid discontinuous shape can be with different shapes, highly, angle or be spaced.In preferred embodiments, the discontinuity surface that each triangle is capable is flat.In another embodiment, Hang one or more discontinuity surfaces or discontinuous shape can be recessed, protruding and/or pitted.In addition, on the bottom that each structure flattens, can deposit the direction that minute shape (for example pyramid or circular cone) is further controlled reflected energy.
In preferred embodiments, the particular community of the material of element printing opacity " main body " is that direction---for example scattering-in minimizes with change with energy absorption.In addition, the material require that is used for element body possesses etching, mold or other changes the needed particular community of processing of element body.The example of suitable material is a polymer, for example Merlon and PMMA (polymethyl methacrylate).Using etching, mold or embossment in element body, to form under the situation of a succession of indentation, can use the such packing material of high reflecting metal.In addition, can use the such pure material of polymer or do not use material (gas, air or vacuum) to fill indentation.Using pure material or do not using material to fill under the situation of indentation, the material refractive index of selecting to be used for element body will be higher than filler.Refringence minimum between filler and the element body is estimated as 0.01.In preferred embodiments, identical for each the shape refractive index in the element body.For purposes of the invention, term reflective also comprises refraction in the light that the irradiating structure main body is discussed, and wherein the difference in the material refractive index obtains actual or the approaching total reflection that is radiated at structural light with incidence angle.
Using reflecting material to fill under the situation of indentation, it is capable to use single material or composite to form triangle above-mentioned.Optimization is used to reflect the packing material of shape, makes to absorb minimum, and has highly reflective for the controlled direction change of energy.The example of suitable material is aluminium or silver, and reflectivity is 95% or bigger, can also be compound adhesive, composite or the composite material with different refractivity or volume reflection.
As mentioned above, reflecting material can be coated on the printing opacity main body, as the part of body recess filler or as with printing opacity main body physical separation but be attached to the end of top refraction structure.
The second method that generates multiple reflection body member preferred embodiment is included in that to generate above-mentioned triangle in the photo-sensitive transparent material capable.Generate the shape of wanting by in the element body specific region, changing refractive index.In this embodiment, close on one side deposition thin layer of reflective material, for example an aluminium of the capable bottom of triangle (reflecting surface) at element.Remove corresponding to triangle capable between at interval deposition region, form a strip pattern across element.The refractive index of using optimization process to change the element specific region needs light-sensitive material to have good optical and engineering properties.Except enough sensitometric refraction rates changed, suitable " writing " wavelength (typical case is in the ultra-violet (UV) band), optical clarity, film formability and the mechanical features of a combination also was very important.Such material can be to have optimized the organic polymer of mechanical features or made up the polyfunctional organic-inorganic mixture of organic polymer chemistry, i.e. polysilane, poly-germane and/or their colloidal sol-gel mixture.
Another with use in the photo-sensitive transparent material related embodiment, discontinuous shape can be with different shapes, highly, angle or be spaced, the one or more discontinuity surfaces that comprise the shape that triangle is capable can be recessed, protruding and/or pitted.In addition, or as mentioned above as the part of deposition processes, or independently handle, can on the one side of the element body directly over each structural base, deposit the direction of minute shape (for example pyramid or circular cone) with further control reflected energy as one.In another embodiment, can be different for each discontinuous shape refractive index, in the element body scope, can produce various alternation patterns like this to reach specific effect.In another embodiment, can use, in the element body scope, generate various patterns by filling indentation shape that obtains and the combination that changes the light-sensitive material refractive index.
Term light comprises corresponding to the electromagnetic radiation that has from the visible wavelength to the infrared wavelength when using in the present invention.But instrument of the present invention can be used for any electromagnetic radiation that can be reflected or reflect, and is controlled by the ability of the structure of size that manufacturing does like this and material.Clear and definite says, the present invention can be used in radio, radar, microwave, infrared ray, visible light, ultraviolet ray, X ray and Ge Ma type ray.
Another method of making structure of the present invention is can make structure by the suitable material of being kept perfectly property in the physics working environment by some, comes suspended structure with some suitable methods then.Suspension can be finished by using the line or certain filament that form grid.This method of the present invention is useful in Application of Solar Energy, and wherein the size of Transflective body is not had the restriction of the size requirements of emission demonstration.
A kind of mirror that is to use in the multiple commonsense method of collection solar radiation reflexes to the pipeline complex with radiation from the sun.The pipeline complex comprises first pipeline of carrying liquid to be heated, by second pipe ring around.Space typical case between two pipelines finds time to reduce convection current and conduction loss amount.By structure of the present invention is installed in this space between pipeline, on the pipeline that most of solar radiation meeting is collected and reflected back is to be heated from mirror, therefore increased gross efficiency.In most of the cases, water back also can emitted radiation, and this also can be collected and reflect back.Therefore the Transflective body is passed in solar radiation, and is reflected back to solar collector together in the radiation that the radiation that begins not to be absorbed by solar collector and solar collector are launched owing to temperature.In this embodiment, vacuum is the transparent material with structurally associated.
In this Application of Solar Energy, the height of structure only depends on the interval between the pipeline, the bottom of structure be used in do not have emission comparing in showing can be big.The width of bottom can be 3500 μ or bigger, though also can use the structure of reduced size for this use.Preferably with a large amount of structural bendings around at least a portion pipeline to improve the collection and the reflection of radiation.
When using in the present invention, term " structure " refers to reflect or the shape of catoptrical element.Structure can be placed on the light transmitting material or among the physical separation composition, it can form or represent with being cut into groove among the light transmitting material or indentation, perhaps it can be the final result of light transmitting material section processes, has formed the shape with different refractivity like this.At transmission material is under the situation of gas or vacuum, resemble in Application of Solar Energy, to find, structure by grid, line, filament or other such equipment be placed on material " in ", grid is represented the surface of Transflective body.
The ability of uniqueness of the present invention is can reflect and the more light of any prior art equipment of transmittance.The percentage of the light that can reflect and with light that can transmission with addition greater than absolutely.