Sizing the primary mirror Cell with GUI PLOP

What is   GUI PLOP:

Gui plop

GUI PLOP is a powerful program for project and quality evaluation of the cell of the telescope's primary mirror mount.

Why can be critical the mechanics of the cell supporting the mirror?

Who's profession is aware that optical precision of an objective quality   reflector telescope “just OK”, is to present a defect ON THE GLASS of its reflective surface (intended as a measurement “peak-to-valley” of its worst bumps on the surface), that does not exceed 68,75 nanometers high., i.e. millionths of a millimeter, that degrade the’ REFLECTED WAVE of a value that is one quarter of the wavelength (Lambda) of 550 NMS   owned by reflected light yellow-green, to which the human eye is most sensitive: That is the famous “Lambda/4.

And this is due to the fact that the wave, in coming reflected, becomes damaged twice by mistake on the glass: A first time in incidence and a second emerging from it.    

And this double damage of the incident wave and emerging shows that to maintain on the wave a lack of reflection of Lambda/4 , It is necessary that the glass possess a Double accuracy, namely Lambda/8, Since:

Lambda/8 + Lambda/8 = Lambda/4.

Obviously, as to reach at least the precision of 68.75 millionths of a millimeter of tolerance, mirror performance can be significantly influenced by strains don't own optics, but induced by a mediocre mirror support, that in his cell may be raised to Flex when varies its pointing to objects that are at the zenith or others who are on the horizon.

These possible downturns generate an additional error that is added to that of its surface, potentially degrading the performance of the instrument.

Who is the author of GUI PLOP?

The program is the brainchild of several people. As man's read in the window “About Plop”, those mentioned first in importance is the author of the program David Lewis and the engineer Toshimi Taki.

The latter is Japanese aircraft designer with the hobby of astronomy, and modified for this purpose a specific tool of modern designers, that is structural calculation method of "Finite Elements" , in order to apply for   design and test the telescope mirror support cells    , in such a way as to minimize the distortions introduced by their solicitations that negatively affect optical performance.

One of these cells support in fact, features support the primary mirror at a number of points in the plane, whose provision is calculated in order to load on each of them, a portion of the weight of the mirror even varying its trim in the telescope pointing, to generate the least distortion of reflective   Republic(in function of the number of support points chosen), and with such distortion seeing the error of optical reflection expressed in RMS, or in ratio values ​​peak / valley, that will overlap with other surface errors, contributing to the degradation of the performance of the instrument.

What is “Finite element structural analysis”?:

It is the study of the behavior under load of a structural element complex urged from its supports (in our case, the mirror) , which is then divided into a NETWORK of thousands of components of a little size, whose behavior under load is describable with the approximation of algebraic equations, only reachable by with the power of current computers. Equations that describe this behaviour, coming to display in different colors on different degrees of deformation of different surface under consideration stressed areas.

What is the utility GUI PLOP for the Stargazer?

The program allows in-depth technical evaluations that go far beyond the knowledge of the normal BASE stargazer self telescope making. However, in the field of amateur astronomy "DIY", PLOP GUI is very useful for the design of the cell size of the primary of your own telescope.

But the use of the program is not so "friendly" and immediate. So not younger people like me, that use it very rarely, over time, forget the "how to".

This is the reason that drives me often to write the instructions "reminder" for the benefit of myself. To fall back in time, in case My of future needs.

This script is then one....

PSEUDO TUTORIAL for using the program   GUI PLOP

…Tutorial here limited to a PRATICAL EXAMPLE of sizing the primary mirror cell Newton Ø300mm with 9 support points (but we will see that at the user is, however, reserved the right to choose A DIFFERENT number of support points desirables, in order to compare their values ​​and choose the optimal one).

1) In the PLOP CELL DESIGNER click on AUTOMATIC CELL DESIGN –

1   2-modif

You open the PLOP AUTOMATIC CELL DESIGNER, where to enter primary diameter 300 mm – thickness 30 mm – focal length 1500 mm – diameter of the secondary mirror 67 mm – leave blank the box hole –

2) click NEXT –

9 mpunti   4

You open the window for choosing the number supporting points of the cell

3) Click the cell to 9 point and click on DONE

4) You open the PLOP RUN CONTROLS where Click START PLOT –

the program processes and calculations when he finished open the communication – PLOT EXECUTION FINISHED –

5) Press OK.

edit as text   graphic plots

6) Return to the main screen and click on the folder/file cabinet DESIGNER PLOP CELL EDIT AS TEXT

Shows you can look in many rows aligned all text/numeric calculation datas, some of which are used here to draw the cell

7) Prepare to draw the cell with a CAD or other hand-drawn method:

8) First draw a circle with diameter of the primary mirror (300mm);

9) Among the many rows colunmed of datas calculation in textual / numerical format, you must search for the variable for calculation of the radius of the internal support named VAR R_INNER 0.331085 – then multiply the radius of the mirror by this coefficient to obtain the radius of the inner circle of the cell on which there are support points.

(150×0.331085=) 49.66mm = radius of inner supports

10) Draw this circle to be concentric to the mirror diameter.

11) Between the same rows in text columns, look then the voice of the outer radius named VAR R_OUTER 0.742219 – multiply the radius of the mirror by this coefficient to obtain the radius of the circle on which there are other points of support.

(150×0.742219=) 111.33mm = radius of external supports.

12) Draw this new circle concentric at the preceeding inner support circle.

13) Go to the MENU mane GRAPHIC PLOTS’ of window PLOP CELL DESIGNER, and click on GRAPHIC PLOTS, then click CELL PARTS:

cell parts posizione triangoli

You will see the location in respect of the mirror were are the three isosceles triangles of support (due to a chosen cell is 9 points that provides in support of the nine vertex of the three triangles).

  14) Click now on GRAPHIC PLOTS and then on PART DIMENSIONS:

graphic plots + part dimensions   coordinate trinagolo

  Data sheet appears to one of three equal triangles, in Cartesian coordinates (in colour black) of the three vertex of support, and centre of gravity (in red) of each triangle,   which will fall on a third unit still to be drawn, lying between the two already drawn to the support points of the mirror.

Look at the BOX on top right, that indicates the position coordinates of the gravity center (CG = Center of Gravity of the piece displayed), given  in coordinates relative to the center of the mirror with:

the X-coordinate of the center of gravity = 80,832 mm and Y-coordinate =   0:

Which means the Centre of gravity is vertically (Y = 0) the Center mirror, at a distance (of RADIUS) from Central 80,832 mm (Coord. Y,):

Distance that identifies this third circle which lies, until 120 degrees away from each other, the three centres of gravity of the three triangles to support mirror.

15) Then draw the concentric circle of radius 80.332mm base of seat gravity points of the three triangles.

Looking at the triangle shape appears, We note that both the vertex and the Centre of gravity are indicated in Cartesian coordinates , but this time refered to 2 (the vertex 2 lower left side) of the triangle, who coordinates X = 0 and Y = 0, indicating the "zero point" of all measurements indicated.

The point 1 (the lower horizontal line) He then X-coordinate = 72,696 and Y = 0 which means you along as his 72,696 mm abscissa, without variations of ordinate (because Y = 0).

16) We write that value not to forget it.

The program offers to display and in the same dialog box, the ROTATE button, and with this function you can rotate the triangle (rotation You will see that occur in counterclockwise) and bring up from time to time each of its three vertices (The first of these was the number 2; the second will be the # 3 and the third on n. 1) in the point at – origin of coordinates X = 0; Y = 0,   that is to the left of the figure-video.

Like this, for each rotation that we will request, you will gradually see the length of the side lying horizontally at the bottom, indicated by its abscissa X.

17) Even those remaining two values   annotate, that the with the first will identify the dimensions of each of the three triangles. (Two of these three values are identical, because it is isosceles triangles).

18) It only remains to draw three triangles to 120° apart from each other, by placing the 6 points related to the extremes of the hypotenuses (of 9 total), on the circumference of the outer radius (VAR R_OUTER =) 111.33mm;

And verify that the three points relating to their heights will lies on the circumference of inner radius (VAR R_INNER =) 49.66mm.

While their center of gravity lies on the circumference of RADIUS 80,832 mm

END OF CELL DESIGN.

If now we go back to point 13) PLOP CELL DESIGNER, and click GRAPHIC PLOTS, We have the opportunity to choose to see other graphic representations of the mirror and its deformation when it were mounted in this designed cell .

The first view can you get by clicking on the drop down menu   MESH GRAPHIC PLOTS, to see how the mirror surface has been divided into polygons of equal area, identified as the “Finite elements” taken into account in calculating.

mesh

The second item of the menu is SUPPORTS, that we had already seen above.

The third item of the menu is stress CONTOUR and will show the "level sollicitation lines" around the support points. A kind of contour lines that indicate the homogeneous level changes (Although infinitesimal) reached by the deformed surface, at constant solicitation.

graphic plots contour

The fourth item in the drop-down menu is interesting COLOURPLOT that will display the map with the amount of deformation expressed even in relationship RMS like “"Efficace value"” of the entire surface, That  at local surface level in the various colors of a scale shown at the side, indicating values ​​PEAK / VALLEYAnd deformation generated  .

colour plot

The RMS value 1.88 exponent-06 detectable in column at the upper right of the graph, indicates the effective value (or deviation) the error produced on the whole surface of the mirror from this cell type, in relation to the wavelength (Lambda) of 550 Nanometers of yellow-green light that the human eye is most sensitive;

While the underlying value P-V   8,397 exponent-06 indicates the error expressed as peak/Valley, or local minimum and maximum deformation of the surface.

In practice, the areas in blue are those less deformed becuase well supported by the support points for the mirror; While the green areas are intermediate strain, and the red ones are those most deformed.

How to get an idea of the goodness of the cell?

Even without resorting to mathematics for a techincally precise quntification, We read the text   help“PloP user.pdf”, the suggestion that an RMS error of 4.2 Exponent-06 mm is corresponding to Lambda / 128, and it is to be considered a limit reasonably good for a cell.

Our cell complaint in the graph an RMS value of 1.88E-06, that is 2.23 times smaller and therefore better, than the limit defined as reasonably good for a cell.

Now that we made an idea of ​​the magnitude of the quality of our cell, we only see what function have the remaining items on the pulldown menu.

We continue and we end up skipping the fifth and sixth voice CELL PARTS and PART DIMENSIONS, both already been seen above., and meet the last entry “Z88” the drop-down menu, which is not of our direct interest as it relates to the use of a software extension called Z88 for “insiders” finite elements calculation.

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