CA1076637A - Shadow mask - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE
In a cathode ray tube having a curved phosphor screen, a shadow mask having bored therein apertures and electron beam generating means for generating three in-line electron beams aligned in a horizontal direction, the apertures of the shadow mask arc aligned along barrel-shaped lines extending in a horizontal direction and are aligned along pin-cushioned lines extending in a vertical direction and the diameter distribution of the apertures is arranged so that the distribution of the electron beam trans-mission factor of the mask is concentric about the center of the mask.

Description

1~'76f~37 - BACI~;ROIJI~D OF THE INVENTION
Field of the nvention This invention relates to an improved shadow mask, and more particularly to a color cathode ray tube in which an improved shadow mask i9 us~sd to ensure thst an electron beam strikes exactly on a color dot of the tube.
Description of the Prior Art Conventional types of color cathode ray tubes comprise an electron gun for emitting an electron beam, a color screen and a shadow mask or aperture grill for beam selection, in which each of the apertures per-forated in the ma~k or grill exactly corresponds to each of the color dots and co-operates to direct the beam precisely onto predetermined color dots for reproducing a color picture, However, the beam separation i9 not carried out accurately due to certain causes that introduce improper ~eparation and or misconvergence, This is especially noticeable in the peripheral areas of the screen.
ST~MMARY OF TH~: INVENTION
The present invention is directed to a shadow-mask type color cathode ray tube in which a plurality of electron beams are deflected horizontally and vertically while being kept aligned in a common plane and are caused to scan an outwardly projecting screen having a spherical or cylindrical curvature or the like, To reach the screen the beams pass through a shadow mask and the transmission factor of the mask i~
increa9ed to provide for enhanced brightness in the reproduced picture.
Accordingly, one object of this invention is to provide an improved ~hadow m ask.
Another object of this invention is to provide an improved shadow mask in which a plurality of apertures are arranged in a particular pattern, Another object of this invention is to provide a novel color cathode ray tube in which an electron beam impinges exactly on a predetermined color dot.
Another object of this invention is to provide a color cathode . .

~ :

~: ' ~(~7t~ 7 arranged in a particular pattern.
Another object of this invention is to provide a novel color cathode ray tube in which an electron beam is exactly impinged on a predetermined color dot.
Another object of this invention is to provide a color cathode ray tube which is bright and free from color misregis-tration.
Another object of this invention is to provide a color cathode ray tube which employs an in-line gun.
Still another object of this invention is to provide a color cathode ray tube employing an improved shadow mask having a plurality of apertures bored therethrough in a particular pattern and color dots closely packed on the peripheral portion of a screen.
In accordance with the foregoing objects, there is provided:
A shadow mask for use in cathode ray tubes comprising a metal plate, and a plurality of apertures of equal diameter through the metal plate, wherein said plate has a transmission-factor at each elemental area and said transmission-factor is related to the location of said elemental area and is propor-tional to the diameter of said apertures in said elemental area and inversely proportional to the spacing between said apertures in said elemental area, and in which said apertures are located .~ ~
at the intersecting points of barrel-shaped horizontal and pin-cushioned vertical curved lines, the horizontal pitches of the apertures being enlarged at both ends of vertical align-ment lines and the vertical pitches of the apertures being reduced at both ends of horizontal alignment lines, the hori-zontal spacing of the vertical curved lines increasing as the - horizontally extending periphery of the shadow mask is ~ -2-7~;37 approached and the vertical spacing of the horizontal curved lines decreasing as the vertically extending periphery of the shadow mask is approached and said transmission-factor varies from one of said elemental areas to another of said elemental areas to form equi-transmission-factor lines in a family of concentric circles substantially symmetrically disposed about the center of the shadow mask.
Other objects, features and advantages of this inven-tion will become apparent from the following description taken in conjunction with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
Figure 1 is a perspective view, partly cut away, showing a cathode ray tube;
Figure 2 is a schematic diagram of a shadow mask used in a conventional shadow-mask type color cathode ray tube;
Figures 3A and 3B are schematic diagrams showing the relative arrangement of picture elements on the screen perpen-dicular to the central axis of a cathode ray tube employing the shadow mask depicted in Figure 2;
Figure 4 is a schematic diagram showing the relative arrangement of the picture elements on a spherical screen used in conjunction with the shadow mask shown in Figure 2;
Figures 5A, 5B and 5C are enlarged schematic diagrams showing the relative arrangement of the picture elements on the screen in accordance with this invention;
Figure 6 is an exaggerated depiction of one example of a shadow mask according to this invention;

'76637 Figure 7, appcaring with F ig 4, shows an enlargement of the relative arrangen~ent of the picture elements on a spherical screen in the case of using the mask exemplified in Figure h;
Figure 8, appearing with Fig. 6 is a schematic diagram illus-trating another example of a mask, according to this invention;
Figure 9 shows the relationship between co-ordinates and the pitches of aperture alignment lines of the mask according to this invention;
Figure 10 is an enlarged schematic diagram showing the relative arrangement of the picture elements on the screen, for explaining this invention, and;
Figu~res llA, llB and llC are schematic diagrams,- for expl~in~ng equi-di_meters of the apertures of the mask of this invention.

:- DESCRIPTION OF THE PREFERRED EMBODIMENTS
For a better undarstanding of this invention, a description will .~ be given first of a shadow mask color cathode ray tube, 11 in Figure 1, which has three electrc~ beams 12, 13 and 14 arranged in line in a common horizontal plane 15. The beams are deflected by deflecting ` ~ 20 means (not shown) horizontally and vertically across a surface 16 per-pendicular to pass through a shadow mask 17 and the central axis of the tube and are thereby caused to scan an outwardly curved spherical ~, screen 18. 3 is a plane perpendicular to the central axis of the tube and if the red, green and blue phosphor dots DR, DG and DB on the screen 3 are formed by the usual light or electron beam printing method employing a light or electron beam passing through the horizontal and vertical de-flection centers of the beams, the phosphor dots D3~, DG and DB of a diameter ~, which form triplets of picture elements for each aperture

2 of the mask 1, are se~uentially arranged on the horizontal lines .

X3, X2, Xl, X0, Xl', X2', X3', .. in the form of horizontal rows of triplets as shown in Figures 3A and 3B. In view of the requirement for closely packed hexagonal arrays of the phosphor dots DR, DG and DB
on the phosphor screen 3, the pitch Lx of adjacent vertical columns of ` - 3-apertures ~f the shadow mask 1 is s~lected to be J~ t'lnes the pitch Ly of adjacent horizontal rows of apertures, In a shadow mask tube 11 ~Figure 1) having a spherical screen and using an in-line gun, the ~eam triplets 10 which strike the screen 18 in line, pass through individual apertures 19 tilted relative to the ori-ginal line of alignment of the three beams as shown in Figure 4. This phenomenon is referred to as the twist of the in-line beam triplets.
The twiRt phenomenon is a purely geometrical effect caused by the com-bination of in-line alignment of three beams and a spherical screen, Considering the coordinate system illustrated in Figure 1, the three beams 12, 13 and 14 passing through the aperture 19 of the shadow mask 17 form the flat plane 16 which is parallel to the x-axis of the tube and which makes an angle of ~v (the angle of vertical deflection) to the x-z plane. This flat plane 16 intersects the spherical screen 18 which has the center 0 on the z-axis, The in-line beam triplet 10 thus strikes inter-section line R . which is an elliptical arc when viewed from the z-axis direction and is expressed as follows, x2 + ( l t ~ ) 2 + 2( R-L) y + L - 2RL = 0 (Eq. 1) tan 9V tanOv where R i~ the radius of curvature of the ~pherical screen 18 and L is the distance from the deflection center of the beams to the center of the screen.
Thi9 is the cause of the twist of a landing in-line beam triplet. The mathematical expression of the angle of twist is obtained by differentiating the equation ( 1 ) and using the relation of tanHv = y / (~/R - x - y - R + L ), Thus, it follows that tan~ ~ Y =_ , _ (Eq, 2) dx R2 _ x2 _ (R - L~ ~/RG XG yG -where ~ is the angle of twist measured counterclockwise from the positive x-axis, The approximate form of the equation (2) is ' xy m~ 7 ~ Eq 3) With the arrangement described, in which the diameter o the phosphor dots DR, DG and DB is selected to be0 the same as described in Figure 3, the phosphor dots corresponding to one of the horizontal rows of apertures G overlàp those of adjacent horizontal rows of aper-tures. This i9 due to the fixed relative arrangements of adjacent aper-tures, as depicted in Figure 5A. To avoid this overlap, the diameter of the apertures of the shadow mask is selected to be small in accordance with the angle ~, and the diameterp' of the phosphor dots on the screen 3 is selected correspondingly. Thus, in a conventional shadow mask with an in-line gun, the beam impact allowance considerably decreases as a consequence of the twist phenomenon of the landing beam triplets (Figure 5A) .
To avoid this, the present inventors have previously proposed in the copending Canadian patent application No. 67, 976 filed November 20, 1969, a shadow mask of the type in which the horizontal alignment lines of the apertures were "barrel-shaped" and the vertical alignment lines o the apertures were "pin-cushioned", In addition, the horizontal and vertical alignment lines of the apertures were orthogonal to each other and the apertures were located at the intersections of the horizontal and vertical alignment lines. The primary object of this shadow mask was to co~npensate the twist phenomenon completely. The philosophy of the shadow mask of our previous invention was to make fit the alignment of the apertures for the geometrical twist of the beam triplets striking the 9creen This meant that a horizontal row of the aligned aperture~
on the spherically-pressed shadow mask and the line pa9sing through the deflection centers of the three electron beams had to be included in a 9ingle flat plane.
/ Considering the fact that the radius of the spherically pressed shadow mask is nearly equal to the radius R of the panel inner surface, and ne-glecting the length of the gap between the shadow mask and the panel inner surface as compared with L, the horizontal alignment lines of the aper-,~, .

1~;'6~;37 ture~ must be the arcs of the ellipses given by the equation ( 1) which is the solution of the differential equation of the geometrical twist. A
conversion of the intcgral constant ~ in equation ( l) yields the following expression 2 R ~ (R _ T ) - 2(R - L)¦R2 _ y 2 2 x + 2 Yo (R - L)- (R - L~;~02 2 -2 ~ - y + L - 2RL = 0 (Eq. 4) Yo where, y~0 for yO~ 0, yO is a parameter which i9 the intercept of the y-axis by the curve The group of arcs of ellipses (Eq. 4) form a "barrel-shaped" group of

3' 2' l' X0~ Xl ~ X2 ~ X3'~ - - - a9 9hown in Figure 6. The vertical alignment line3 of the apertures must be made "pin-cushioned" so as to be orthogonal to the horizontal alignment lines through-out the 9hadow mask plane The vertical alignment line9 can be obtained by solving the following differential equation which is the inverse, and has the oppo9ite sign, of the equation of geometrical twi~t (Eq 2) dy R2 _ x2 _ (R - L)/R2 _ x2_ y2 (Eq. 5) ,'~. .
The solution of the equation (5) is obtained as follows.
t ~
~R (R L) ¦R X Y J( R L
R (R L) R XO
20¦¦R x2 y ~ ~ (Eq. 6) where xO is a parameter which is the intercept of the x-axis by the curve Thus, curves obtained from equation (6) make just right angles to the group of curves obtained from equation (4) throughout the whole shadow mask i~6f~37 plane. Equation (6), hc)wever, has thc iollo~ving approximate ~orm which causes an error of + 1, at most, in the orthogonality between the hori-~ontal and vertica1 alignment lines, x x o + /~ x 0) Y (Eq, 7 for xO ~ 0 This is the "pin-cushioned" group of circular arcs .,.., Y3, Y2, Yl, Y0, Yl', Y2', Y3', .. as shown in Figure 6.
Equations (4), (6) and (7) were derived on the basis of the spheri-cally pressed shadow mask. These equations relate to the alignment lines of the apertures onthe spherically pressed shadow mask when viewed from the z-axis direction, However, considering the experimental result that when a flat shadow mask is pressed into a nearly spherical surface, the displacement of the aperture position occurs almost only in the z-direction and the displacement in the x-y plane is negligibly small. These equations can be interpreted to mean the alignrnent lines of the apertures on the flat (pre-pressed) shadow mask, The foregoing description has been based on spherical phosphor screen 3. The 9ame principle~ apply in the case in which the screen i8 a cylindrical surface extending in a vertical direction. In this case, however, the relationship of the inclination angle of the horizontal row of the triplet of the phosphor dot3 DR, DG and DB co the horizontal line for each aperture 2 of the mask l is as follows.

dy xy tanO =~
dx R2 _ x2 _ (R - L) ~ _ x2 (Eq, 8) corresponding to equation ( 2) .
Accordingly, in this case the horizontal alignment lines of the apertures are made "barrel-shaped"; and the vertical alignment lines of the apertures are made "pin-cushioned" so as to be orthogonal to the horizontal alignment lines throughout the shadow mask plane. The aper-tures are positioned at the intersections of the horizontal and vertical iO'7~ 7 alignment lines. The curve of the horizontal alignment lines is obtained by solving the differential equation (Eq 8) to obtain an equation corres-ponding to equation (4) and by satisfying the resulting equation. The curve of the vertical alignrnent lines is obtained by solvingthe following differential equation which is the inverse and has the opposite sign of equation ( ~):

dy R2 _ ~S2 (R - L) ~ (Eq- 9) dx xy to obtain an equation corresponding to equation (4) and by satisfying the resulting equation. Thus, the same results can be obtained as in the previous case.
Although the foregoing discussion has described the shadow mask of the aforementioned copending application in connection with the case where the electron beams respectively corresponding to red, green and blue colors enter the position of the horizontal and vertical deflection means while being aligned in a common horizontal plane, the mask is also applicable to the case where these electron beams enter the position of of the deflection means while being aligned in a common vertical plane.
In this case, it is necessary, of course, to form the apertures at inter-sections of the horizontal alignment lines made "pin-cushioned" and the vertical alignment lines made "barrel-shaped" and to exchange the cur-ves of the horizontal and vertical alignment lines.
As shown in Figure 6 the pitches of the apertures 2 on the horizontal and vertical alignment lines X0 and Y0 on the mask 1 are respectively xO0 and Y0O (xO0 -~0) peculiar to the x- and y- axis. The apertures on each vertical alignment line are arranged at regular intervals and the pitches of the apertures 2 between the vertical alignment lines are gradually increased according to the distance from the center of the mask 1. The pitches of the apertures 2 of the horizontal alignment lines are substantially constant from the center of the mask 1. However, this does not provide the aforementioned relationship that the pitch Lx o~ adjacent vertical columns of apertures of the mask 1 be J~times the pitch Ly of adjacent horizontal rows of apertures at places remote :.
from ~ - 8 -1~7~37 the center of the mask ~.
Thus, in Figure 6 a~ertu-es are arranged at regular intervals alor.g the axes X0 and Y0 and the pitches of the aper-tures between the vertical alignment lines increases as the dis-tance from the center of masX 1 increases. In Figure 8, however, the intervals between the apertures along the axes Y decreases as the distance from the center of the mask increases. In other words, in the Figure 6 embodiment, the apertures have constant spacing along the X0 and Y0 axes, whereas in the Figure 8 em-10 bodiment has varied spacings along both the X0 and Y0 axes so that the colour dots can be more closely packed on the peripheral portions of the screen than in the Figure 6 embodimen'.

' C
- - 8a ~l~t7~37 Consequently, the hori~ont~l rows OL the triplets of th~ phosphor dots DR, DG and DB l~id down on th~ screen 3 at places remote from the center of the n~ask 1 tilt against the h.~rizontal lines and do not overlap adjacent c3ots as depicted in Figure 7. The vertical 3pacings of the phosphor dots are reduced as compared with the vertical spacing at the center of the screen and the horizontal spacings of the dots are enlarged a~ compared with the horizontal spacing at the center. This does not fully satisfy the requirement for clo~ely packed he~agonal arrays of the phosphor dots and introduces the possibility of deterioration of color ~urity resulting from overlapping of the phosphor dots of adjacent hori-zontal rows of the triplets at places more remote from the center of the screen than the above-mentioned ones as shown in Figure SC.
In view of the foregoing, the present invention has for its object the improvement of the shadow mask of the type depicted in Figure 6 ~or u~e with a shadow mask color cathode ray tube of the type in which the red, green and blue electron beams, aligned in a common horizontal ;, plane, are deflected by deflection means horizontally and verticaPy, still in a common plane, and are thereby caused to scan an outwardly curved spherical screen through a shadow ma~k. The shadow mask of this invention is featured first in that the pitches of the apertures are en-larged at both ends of the vertical alignment lines and the horizontal pitches of the apertures are enlarged at both ends of the ver-tical alignment lines and the vertical pitches of the apertures are reduced at both ends of the horizontal alignment lines.
The horizontal spacing of the vertical curved lines in-creases as the horizontally extending periphery of the shadow mask is approached and the vertical spacing of the horizontal curved lines decreases as the vertically extending periphery of the shadow mask is approached.

~j _ g _ -C /~

_ .

The shadL)w rnask of the present invention is further arranged so tha.t the diameters oi the a~ertures of the shado~r~ ma3k vary to providc equi-transmission-factor curves of the electron beams through the shadow mask as shown in Figure 10, such curves rnay be circles 70 which are concentric substanti.al].y about the center of the shadow mask 1. The transmission factors of the apertures are reduced from the center of the mask to the peripheral portion thereof. There are several reasons ~vhy C
. - _ 10'~
the equi-trAnJmissio~-factor curves of the electron be~ms are in the form of circles substantially concentric about the centcr of the shadow mask. One reason is that rcspective portions of the color cathode ray tube are usually formed chiefly with parts symmetrical about the axis of the tube. Especially when the screen and the shadow mask are spherical, substantially the entire construction of the cathode ray tube i8 symmetrical about the axis thereof. Deterioration Gf color purity on the 9creen varies concentrically outward from the center of the screen due to errors in the mechanical precision of the parts and their arrangements, thermal deformation of the shadow mask, the influence of earth magnetism and so on. As a result, it is convenient to make the equi-transrniasion-factor curves of the shadow mask for the electron beam in the form of circles concentric about the center of the mask for compensation of deterioration of the color purity. Even if the luminance distribution of the screen is concentrically circular about its center when the equi-transmission-factor lines of the shadow mask for the electron beam, substantially no appreciable change in vision is caused in the re-produced picture as compared with the cases where the luminance distri-- bution i9 not concentrically circular.
A description will be given of the respective enlargement and re-` duction of the pitches of the horizontal and vertical alignment lines of the _ apertures from the center of the mask toward both ends of the horizontal and vertical center alignrnent lines. The method for obtaining the varying values of the pitches for such pitch distribution has been proposed in the aforem entioned appli cation Se rial No . 67, 9 7 6, filed N ovembe r 20, 19 69 but also be described below, In Figure 9 horizontal and vertical alignment lines running across the aperture 2 at a desired point P on the mask 1, re9pectively based upon the aforementioned equations (4) and (6) are respectively designated by X and Y . The intersecting point of the line X with the y-axis ~Y0) is indicated by B( 0, y ) and the intersecting point of the line Y with the x-axis is identified by A ( x, 0 ).
. ' Assume that alQ~o66r~l7ate o the point ~ i5~X( n, m ), y ( n, m)} ., Since the point P is the int~rsccting point of the alignment lines Xm and Yn, the aforementioned equations (4) and (6) are expressed as follows, by substituting Ym and xn for yO and xO in equations ~4) and (h), respectively, and by approximately solving simultaneous equations derived therefrom.

~!,e x( n, m ) ,( 1 + Y ) x .. .............(10) x 2 n y ( n, m ) -~( 1 2RL) Ym The solution of the simultaneous equations derived from the equations

(4) and (6) results in a power series of variables such as x , Y2 ~

xy x2 v2, xy, ............... whose numerators are terms of second order R RL RL RL
order with respect to a length on the shadow mask plane and whose de-nominators are terms of second order with respect to the length of the radius of curvature R of the spherical screen or the distance from the deflection center of the screen or both of them. The higher order terms are neglected in the approximation for obtaining equations ( 10) and ( 11), since the aforementioned variables are less than 0. 2 in practice.
Accordingly, if the pitches of the vertical and horizontal align-ment lines of the apertures in the vicinity of the point P are taken as - PH ( n, m ) and PV ( n, m ) respectively, they are given by the following equation9. y 2 P ( n, m ) = x(n, m ) - x( n-l, m ) = ( 1 + ) ( x - x ) . .. (12) H 2RL n n-l PV ( n, m ) = y (n, m) - y ( n, m- 1) 2RL ) ( Ym ~ Ym_l ) -...... (13) In thi9 case ( xn - x 1) is the pitch of the vertical alignment lines on the x-axis ( X0 ) and may be expressed by PH ( n, 0 ), while ( Y ~ Y 1) i9 the pitch of the horizontal alignment lines on the y-axis ( Y0 ) and may be expressed by PV ( 0, m ) Consequently, equations ( 12) and ( 13) are respectively given by the following equations ( 14) and ( 15), .

.. . . . .. ... . . ~ _, ~ .' ~

1~76~37 Y ,.
PH ( n, m ) = ( 1 + 2 ) PH ( n, 0 ) ..... ( 14) PV t n, m ) = ( 1 ~ 7RL ) P~ ( 0, m ) .. .(15) With a line y = a~x joining the center of the shadow mask 1 with its peripheral region being expressed in the form of a functional equation, the pitches of the vertical and horizontal alignment lines of the apertures PH ( n, m ) and PV ( n, m ) on the line y = ~x, which are obtained by the above equations ( 14) and ( 15), are selected equal to those PH ( 0, 0 ) and PV ( O, O ) at the center of the mask 1. This implies fulfilment of the requirement for a closely packed array of the apPrtures.

Accordingly, if PH ( n, m ) and P~ ( n, m ) on the line y =~x defined by the equations (14) and (15) are respectively expressed as PH ( n', m' ) and Pv ( n', m' ), it is sufficient only to satisfy the following equations.

PH ( n', m' ) = PH ( 0, 0 ) ............. (16) PV ( n~, m~ ) = PV ( ' ) . . . ' ' . ' . . ,,,,,, .(17) Calculated by using the above relations from equations ( 14) and ( 15), PH ( n, 0 ) and PV ( 0, m ) are given by the following equations.

.
PH (n', m' ) PH ( . ) PH ( n, ) = 2 = 2 - - - - - - - .. .(18) 1 + Ym 1 + Ym :
PV ( n', m' ) Pv ( ~ ) .. .............. ( 19) ; 1 _ n xn : 2RL 2RL
~ F rom equations ( 10) and ( 11) the following relation is obtained:
... 2 x y y(n, m) /(1-2E~ ) - 20 m = L ............ . ( 20) x ( n, m ) / ( 1 + 2Ym Con9ideringy =~x, equation(20) is expressed as follows:

:, . .
.. . .

1(~7f~37 m Y ( n', m' ) / ( 1 _ n ........... ¦21) Xn x ( n', m' ) / ( 1 + 2R

The relation y =~ x is givèn by the following equation y( n', m' ) =yx( n', m' ) .......... (22) Accordingly, the following equation i9 obtained from equations ( 16) and ( 17): 2 Ym Ym = ~ ............................. (Z3) ( 1 n Equation (23)is expressed approximately as follows:

+ 2RL ( Y + x ~ ............... ~24) Further, equations ( 18) and (19) are respectively expres~ed as including y and x . Equation (22) may be substituted into the afore-mentioned equations ( 10) and ( 11) and approximation similar to that for obtaining equations ( 10) and (11) carried out to express equation ( 18) as including only x and equation ( 19) as including only y . PH ( n, O ) and PV ( O, m ) are then given by the following equations.

PH( ~ ) . 2x 2 PH ( n, O ) = 2 ~PH ( . O ) ( 1 ~ ~ 2RL ) . . . . (25) 1 +~2 n p ( O 0) 2 P ( O m ) = V - 2 - ~PV ( , O ) ( 1 + 2 ) .... (26) 1 _ m 7 2RL

~ 2RL

The equatic~ns (25) and (26), thus obtained, respectively represent the pitches of the vertical and horizontal alignment of the apertures on the -... . . . . _ . . _ . -- .. . , .. .. . ",.. y ~ . ' ln~7~37 x- and y-axis when PH ( n, m ) ~?nd PV ( n, m ), at the point P on the line y = x on the mask plane, are equal to P ( 0, 0 ) and P ( 0, 0 ) at the center of the mask.
The equations (25) and (26) are expressed as including~ used in the line y = Xx. If the vertical and hori7.ontal alignment lines of the apertures at the desired point P on the maslc plane, given by the equations (14) and (15), are e~panded by substituting equations (25) and (26), equations ( 14) and ( 15) are then expres3ed by the following equations.

PH (n~ m ) = PH ( , ~ ) ( 1 + m ) ( 1 _ ~,2-- ) (27) Pv( n~ m) =Pv( ~ )( 1 _ _)( 1+ ) ----- (28) Accordingly, if ~ used in the line y =7 x is selected to be equal to 1, the following relation is obtained from equations (27) and ~28).

H( ~ m ) p ( o, o ) -,-- ......................... (29) Pv( n, m) P~( 0, 0) The equations (25) and (26) are respectively expressed by the following equations for x and y n x = 5~ PH ( k, 0 ) . n . k= 1 . n x 2 nPH ( - ) - PH ( ~ ) ~~ -- ..... ~ ~ ~ (30) k= 1 m Ym ~ PV ( , k ) k= 1 m y 2 = mPv ( 0, 0 ) ~ P ( 0, 0 ) ~ 2RL ' ' . (31) :; k= 1 By substituting the x and y into the aforementioned equations (25) and n m . ~, ' . ' .

(26) and p~:rf~rming ,lppro~;inl~tion similar to that for obtaining the aiore-mention~d equations ( 10) ancl ( 11), the following equations are obtained.
{PH ( ' ) }
H ( n~ o ) = PH ( 0, 0 ) ( 1 _ 2RL ) ......................... (32) ~,-r ~ ~Pv(O~O)) PV ( , m ) = PV ( , 0 ) ( 1 + m ) ........................... .(33) Although x and y are expressed in the following forms based upon the equations ( 30) and ( 31) n ~ P ( k, 0 ) k= 1 m Ym PV ( , k ) k= 1 they may be expressed approximately as follows:

n ,~n x = ~ PH ( k, ) ;¦ PH ( k, 0 ) dk ., ..... (34) k= 1 0 m m 10 ~ Ym ~PV ( . k ) ~ PV ( , k ) dk ..... (35) k= 1 o ... .
Substituting k ' s in the equations ( 34) and ( 35) for n and m, respectively, and calculating the equations by using the relations of the equations (32) and (33), the following equations are obtained.

~p ( o, o )~ 2 x = nPH ( 0, 0 ) ( 1 _l 6 ~n ) - - - - - - - - - (36) fPV( ' )} 2 y = mPv ( 0, 0 ) ( 1 + m ) .. , .... (37) Since ~p ( O, 0)~ 2 ~,p ( 0, o)~2 ¢ =~ H ~ and ~!3 = V

the following equations result --- -1 5 ~ 6637 ~ ~~ ~ ~~- - - - r~--~-~

x = nPH ( 0, 0 ) ( l - 4 n ) ...... (38) y = mPv ( 0, 0 ) ( l ~ ~ m ) ...... .(39) Based upon the foregoing, the shadow mask of this invention i8 of such a construction, as depicted in Figure 8, in which the pitches of the horizontal and vertical aligr~nent lines of the apertures on the vertical and hori~.ontal aligr~nent lines passing through the center of the mask are respectively increased and decreased as both side edges of the mask are approached from its center, in a manner to satisfy the aforementioned equations (25) and ~26) or (38) and (39).
The foregoing has described one feature of this invention and the following will hereinafter describe the second feature of this invention such that the equi-transmission-factor curves of the electron beams through the shadow maslc are circles substantially concentric about the center o~ the mask as indicated by 70 in Figure 10, A description will be given of the manner for obtaining the diameters of the apertures for :` this purpo9e.
: As previou91y described in connection with Figure 9, the co-ordinate of the desired point P on the mask l is taken as P{x (n, m ), y (n, m~
- the pitch of the horizontal alignment lines of the apertures in the vicinity 20~ of the point P is PV ( n, m ) and the distance between ad jacent apertures . 2 on the alignment line Yn near the point P is P ( n, m ). In such a case, ~: as previously described in connection with the construction of the mask of Figure 6, the horizontal alignment lines are inclined at an angle 0 to the horizontal line ( the x-axis X0 ), as expressed in the aforementioned equation (2), so that the vertical alignment lines are also inclined at an angle ~ to the vertical line ( the y-axis Y0 ). Accordingly, P ( n, m ) is given by the following equation.
2P ( n, m ) P ( n, m ) = - ............ (40) cos By the way, - 16- 107~i637 - - :
... . .. . . , ,, .~ . ~
~ -cos ~ = ~ ............... (41) 1 ~ tan and tan ~ is given by equation (2) but this equation (2) may be rewritten as ollows, by approximation neglecting terms higher than second order as was done in obtaining the equations ( 10) and ( 11).

xy tan ~ . ~ RL (42) Accordingly, the following equation is obtained by substituting equation (42) into (41) - cos o = l ~ l ( xy )2 , (43) //;~+ ( ~L
since ~l - u ~~ l ~ 2 when u is selected to be a desired small number.
Neglecting ( RY ) in the right side of the equation (43) by approximation similar to the above-described one, it follows that cos ~ ~ l .,,. ............ ,,,........................ .(44) Therefore, the equation (40) i9 rewritten as follows:
P ( n, m ), 2PV ( n, m ) ...................... ....... .(45) While, PV ( n, m ) is expressed by the following equation ~15) previously mentioned, 2 x V ( . m ) ( 1 ~ 2RL ) PV ( ~ m ) ., ... .. . ( 15) and PV ( 0, m ) in the equation ( 15) is given by the following equation ( 26) previously referred to, P ( O, O ) PV ( - m ) = ~ ........... ,... , (26) 1 _ m ~y 2RL

If ~ u9ed in y = ~'x in the equation (26) is selected as l as previously described, the equation (26) can be rewritten as follows:

p~ ( O, O ) PV ( 0. m ) y 2 - - .............. .. , (46) l- m Here, the following equations are respectively obtained from the equations ( lO) and ( 11), ~0~76637 x ( n, m ) Ym x - -, ( 1 ~ ZR ) x ( n, m ) .... (47) ZR L

y ( n, .n ) ` ~ xn2 Y ~ 2 ~ ( 1 + 2RL ) Y ( n~ m ) .. .(48) Xn Accordingly, by approximation similar to the aforementioned one, equations - ( 15) and ( 16) are respectively rewritten as follows:

(x ( n, m )) P ( n m ) - ~1 - 2RL ~ PV ( , m ) .... ,, (49) V 1 ( Y ( n, m ) Consequently, the following equation is obtained from the above equations - (49) and (50), (x ( n, m )) Pv ( n~ m ) ~ ( ( m )~2 PV ( ~ ) f 2 2 ` l Y ~ n~ m ) - x ( n, m ) PV ( ~ ) . . . (51) Substituting equation (51) into equation (45), )) 2 ( ) 2 P ( n, m ) = 1 + 2RL 2PV ( 0, 0 ), . . (52) Since PV ( . 0 ) is the pitch of the horizontal alignrnent lines of the apertures at the center of the shadow mask, 2PV ( 0, 0 ) is the distance between adjacent apertures on the vertical alignment lines at the center of the mask. Accordingly, if this distance between ad jacent apertures is taken as P ( 0, 0 ), P( 0, 0) =2PV( 0, 0) .. ,.......... ,, (53) Further, if P ( n, m ), x (n, m ) and y ( n, m ) in equation (52) are res-.
A

pectively ~xprcssed as P 1 x, y ), x and y, equation (52) is rewritten as ~ollows: 2 2 P ( x, y ) = ( 1 + ~ 2RL ) P ( 0, 0 ) .. , . ..... , (543 Thus, the distance P ( n, m ) between adjacent apertures on the alignment lines Yn near the point P IS obtained as P ( x, y ) by equation (54). A
description will be given of the distribution of the diameters of the apertures each spaced apart from adjacent ones the distance given by equation ( 54).
Where the equi-transmission-factor curves of the shadow mask for the beams are circles concentric about the center of the mask as shown .
in Figure 10, if the distance from the center of the mask to a desired point thereon i9 taken as r, the beam transmission factor at the desired point may be expressed by the following equation in the form of a function T ( r ):
of r:
T (r) = T (0) ( 1 - kr ) .. (55) ---^where T (0) is the transmission factor of the mask at its center and k is a constant.
Tf the diameter of the aperture 2 at the position where the distance between adjacent aperture is expressed by P ( x, y ), namely at the co-ordinate P, is taken as D ( x, y ) and if the tranqmission factor at the . co-ordinate P, considered as the ratio of the 9um of the areas of the ad-jacent three apertures to the areas of an approximate equilateral triangle , . . .
defined by the adjacent three apertures, is taken as T ( x, y ), the trans---mission factor T ( x, y ) is given by the following equation.

T ( x, y ) = J~n { D ( x, y ) } ,, .,, ..., ,, .. (56) While, since r2 = x2 + y2 from the equation (55), T (r)~ that is~

T ( x, y ) can be expressed as follows:

T ( x, y ) = T ( 0, 0 ) ~1 - k ( x2 + y )~ ,,, ,,,,, (57) where T ( 0, 0 ) = T (0), Accordingly, D (x, y ) is given by the following equation from . equations (56) and (57), .. . .
A

t ~/ 6T ( 0, o ) ~ k ( x2 + y2 ~¦ P ( x, y ) ., ., (58) Generally, when u is selected to be a desired small number and ~u -~1 ~ 2 ~ 90 that equation (58) can be expressed as follows:

~i,/6T ( ~ ) ~1 k ( x2 + y2 )lp ( x, y ) ..,., (59) Since equation (59) is based upon equation (55) which is true in the case where the equi-transmission-factor distribution is in the form of circles concentric about the center of the mask, it will be apparent that the dis-tribution of the aperture diameters can be obtained by substituting into equation ( 59) equation ( 54) representing the distribution of the distances between the apertures Accordingly, the following equation i9 derived : from equations (54) and (593 D ( x, y ~ ~ ( X2 1 yZ ,3 {I I Y X ~ , ..... (60) If the diameter of the aperture at the center of the mask i9 taken as D ( 0, 0 ), rT ( O ) D ( 0, 0 ) = / P ( 0. 0 ) ............. (61) ... ,, \l ~
since D ~ 0, 0 ) is the value when x = y = 0 in equation (60).
. , -Therefore, e~ressed by using equation (60), equation (61) is given by -the following equation, ~1 k ( x2 + y2 ~ ( 1 + Y ) D ( 0, 0 ) .... ( This is the equation representing the distribution of the diameters of the : apertures The following description will be made of the equi-diameter lines of the apertures, The equi-diameter lines of the apertures are those loci at points where the ratio of the aperture diameter D ( x, y ) at any point on the mask to the diameter D ( x, y ) at the center of the mask has a constant value ( referred to as a ), namely those loci satisfying the following - 20 - 1~)>76t;37 equati on D ( x, y ) .............. (63) D( 0, 0 ) Accordingly, by sub~tituting equation (63) into equation (62), the equi-diameter lines of the apertures in this invention is given by the following equation.

2 ( x + y ~ YzRL ) = a ............... (64) Generally, in the shadow mask the beam transmission factor at the peripheral region is usually reduced by 30 to 40% as compared with that at the center, so that a maximum value of k ( x2 + y2 ) in the equation (57) is expressed by 0, 3 to 0.4, while a maximum value of ( x2 + y ) is nearly equal to the square of the shortest distance L from the electron beam deflection center to the screen and hence can be given by the following equation.
k~ x2 + y2 ) ~ kL2 = 0.4~0 3 .. , , .............. (65) Further, the radius of curvature R of the screen is usually two to three times as long as the distance L and k has a value n2early2 equal to 1 /RL.
Therefore, the term k2 ( x2 + y2 ). The factor Y2RL can be ne-glected when equation ( 64) has been expanded and equation (64) can then be - expressed as follows:

1 + Y _- x k ( 2 + y2 ) `_ a .............. ..(66) Rearranging equation ( 66), the following equation is obtained.

( k + _ ) x2 + ( k - 1 ) Y = 2 ( 1 - a ) .. , .. ( 67) This is the equation for the equi-diameter lines of the apertures.
Thus, the equi-diameter lines of the apertures in this invention can be obtained. As will be seen from the equation (67), when k>-- .................. t68) RL

the equi-diameter lines form ellipses substantially about the center of the mask 1, as indicated by reference numeral 111 in :Figure llA.

: ` .
- 21- 1~'7~i637 . . - ' ` .

12 ( 1 - a ) Each of th~s~ ellipses has a lunger diametcr 21 and a ~/ k- --shorter diameter 2/ ( ~ and the diameters of the apertures ~/ k + _ RL

are reduced as the peripheral region of the mask is approached from its center, In the case of k having the following value k = - ...................... (69) RL

the equi-diameter lines are straight lines parallel with the y-axis, as indicated by 112 in Figure llB, such that the diameters of the apertures are reduced as they go away from the y-axis. In the case of k having the following value k<RL ,,,,,,,,,, (70) the equi-diameter lines o those apertures having larger diameters than that of the aperture at the center of the mask form hyperbolas about the y-axis, obtained by calculating a from equation (63) as indicated by re-ference numeral 113 in Figure llC. Each has an asymptote Y =--¦~ 1 + k-) x //( RlL ~ k ) and the diameters of the apertures - are increased as they go away from the center of the mask, while the equi-diameter lines of the apertures having smaller diameters than that of the aperture at the center of the mask form hyperbolas about the x-axis, such as indicated by reference numeral 114 in Figure llC, each of which has an asymptote is similar to the aforementioned and the diameters of the apertures are reduced as they go away from the center of the mask.
With the present invention above described, the transmission factor of the electron beams through the shadow mask is enhanced to pro-vide the reproduced picture with brightness and the equi-transmission-factor curves which are circles sub~tantially concentric about the center of the shadow mask readily compensate deterioration of the color purity, thus ensuring a color picture of good quality.

107663'7 - r~ -It will be ~Ipparent th.-t many modifications and variations rnay be effected without departing from the scope of the novel concepts of this invention .

:: , ;i - 23 -11~76637 . ~

~ . .
,

Claims (4)

The emnodiments of` the invention in which an exclusive property or privilege is claimed are defined as follows:

1. A shadow mask for use in cathode ray tubes comprising a metal plate, and a plurality of apertures of equal diameter through the metal plate, wherein said plate has a transmission-factor at each elemental area and said transmission-factor is related to the location of said elemental area and is proportional to the diameter of said apertures in said elemental area and inversely proportional to the spacing between said apertures in said elemental area, and in which said apertures are located at the intersecting points of barrel-shaped horizontal and pin-cushioned vertical curved lines, the horizontal pitches of the apertures being enlarged at both ends of vertical alignment lines and the vertical pitches of the apertures being reduced at both ends of horizontal alignment lines, the horizontal spacing of the vertical curved lines increasing as the horizontally extend-ing periphery of the shadow mask is approached and the vertical spacing of the horizontal curved lines decreasing as the ver-tically extending periphery of the shadow mask is approached and said transmission-factor varies from one of said elemental areas to another of said elemental areas to form equi-transmission-factor lines in a family of concentric circles substantially symmetrically disposed about the center of the shadow mask.

2. A shadow mask as claimed in Claim 1 wherein said apertures are of differing diameters and those apertures of equal diameter lie along common elliptical paths, at least one of the axes of each of the ellipses being horizontal.

3. A shadow mask as claimed in Claim 1 wherein said apertures are of differing diameters and those apertures of equal diameter lie along substantially parallel straight lines in a vertical direction.

4. A shadow mask as claimed in Claim 1 wherein said apertures are of differing diameters and those apertures of equal diameter lie along hyperbolas symmetrically formed about a vertical and a horizontal line.