Application possibility of 3.8 m telescope for radio telescopes

20150730

Mikio Kurita

Kyoto Univ.

Optical and Radio Telescope

Optical Radio

Similarity • Cassegrain system Primary and Secondary Reflector • Alt-Az mount Difference • Wavelength Accuracy of Refs. • Size of primary Ref. • F-ratio Length between the Refs. →location of Altitude axis and Nasmyth focus • Enclosure

Introduction

Cost scaling law Single is more economy.

Minel 1981

∝D2-2.7

Belle & Minel 2004

∝D2.45

• Important thing is innovation which shift the line to downward.

Cost scaling law

∝D2.45

National foundation is weakly limited Technology to break size limitation is more meaningful than technology to cost reduction

In optical telescope, innovations happened in • mount type(Equatorial to Alt-Az mount) • F-ratio (3 to ～1) • Mirror configuration (monolithic to

segment or multiple mirror)

Quiz Which direction is stiff?

𝑓 𝑓

Quiz Stiffness of cantilever

F

When you load constant magnitude force on the end of the rod, and change the direction of the force. What shape of trajectory does the end draw?

Quiz Stiffness of cantilever

Quiz Stiffness of cantilever

Every end describes a circle

Quiz more general shape

A: Ellipse Ellipse is more general

Quiz more general shape

Displacement ellipsoid in case of 3-D

Under condition of

• constant boundary condition

• elastic body

(follow the Hooke’s law)

• concentrated load and volume force

国宝東大寺南大門金剛力士像

An arbitrary point on any object follows the law.

Displacement ellipsoid Application

• Deformation can be grasped by analysis in three elevation angle.

• Sag of the dish is axis-symmetry.

• Notice: The boundary condition must be constant or approximately constant to the whole structure.

Natural Frequency

• Natural frequency indicates the mass-stiffness ratio of the structure

• Natural frequency of truss structure depends its geometry only

=

Stiffness of truss structure against gravity

> =

Cross section scaled

>

Cross section scaled

Natural Frequency with mass

Now you design the supporting structure (purple members) for the box structure. Which structure have higher natural frequency? How size of the cross section of the member is more moderate?

3-bipod 4-bipod 4-tripod

Natural Frequency with mass

mM

ff

c /1

max

Nat

ura

l fre

qu

en

cy

Mass of purple member: 𝑚 (proportional to the cross section)

Natural frequency can be described by only two parameters 𝑓𝑚𝑎𝑥 and 𝑀𝑐 , which are governed by geometry of truss structure Once you decide the geometry, the highest natural frequency can be estimated by 𝑓𝑚𝑎𝑥 We can estimate the character of the structure from this curve

Highly optimized but fragile

Safety

Higher frequency available but confusing

3.8 mTelescope

Aperture: 3.8 m

Focus: Nasmyth × 2 F/6

Field of view: 10’ , 1°

Observational

Wavelength: 0.4 to 4.2 um

Adaptive Optics: J, H bands

Pointing speed < 1 min (whole sky)

Elevation speed 2°/s

Azimuth speed 3°/s

8 m

8 m

20 ton

Mirror Factory

• A venture company was newly build for research and development of large optical elements.

• We aim to shorten processing a large optical element with high precise grinding system instead of polishing.

Facility Astroaero Space Inc.

Grinding Machine （N2C-1300D）

Machining and Test System

10 m

Interferometer &

Anti vibration system

Grinding Machine

Chamber T:23±0.1 deg

Mirror Factory

Motion accuracy of the grinder

1um

Typical error in P-V = 0.1 um/m ※The value includes the error of the gauge

Mirror Factory

Grinding accuracy

Grinding P-V = 0.4um

• Size: Φ610

• Form: Flat

• Material: Clearceram

(zero expansion ceramics, OHARA)

• Processing time: Few hours

Mirror Factory

Problem of Direct Support

The error induced by a direct support comes up to several microns, in case of large but thin optics.

Before setting

After setting (Stress loaded)

Grinding

After grinding (Stress released)

Mirror Factory

blank

machinery table

Kinematic Support Grinding

• Three fixed points for kinematic support (without over constraint). • Multi springs to assist of the support and to decrease friction

between the segment and fixed points • The deformation induced by grinding pressure was simulated

beforehand, and then a stone is controlled to correct the deformation.

Segment

Fixed point

Fixed point

Spring Spring

Without correction

With correction

Figure Error

Mirror Factory

Kinematic Support Grinding

Deformation map with grinding force of 5N

P-V = 5 um The black points show the position of fixed points

Figure error without the grinding pressure correction Each color of the lines corresponds to that of the right figure (1div = 1 um)

Mirror Factory

6 μm

Kinematic Support Grinding

Figure error with the grinding pressure correction Each line is described in a same manner of the preceding page

(1div = 1 um)

Error map -1 um to 1 um

Mirror Factory

Test the Mirror CGH Interferometer

Test beam Goes through the CGH as 1th order and back through as 0st order Reference beam Goes through the CGH as 0th order and back through as 1st order • Semi common pass → Robust against turbulence and vibration

Reference

Imaging lens

Test the Mirror

CGH (Computer Generated Hologram)

Grating

1st order diffraction

Incident

Designed grating pattern produces intentionally distorted wave front

CGH (Computer Generated Hologram)

CGH for the inner (left) and outer (right) segments Each line represents 30 lines in the real pattern

Figure error of the mirror (Structure Function)

Requirement

Result

10

100

RM

S e

rro

r (n

m)

Separation (m)

1 0.1 0.01

Test the Mirror

Mechanical Probe System (under developing)

• Applicable to freeform – Interferometer needs each reference surface meeting test surface

• Wide range and area

• Robust to the environment

• Small Linear stage

Rotary table

Probe

Test the Mirror

Mechanical Probe System Result of φ800 Spherical mirror

Figure map integrated 60 lines scanning The mirror supported by three points (indicated red points)

p-v 900nm Deformation by three point supporting （FEM simulation）

Test the Mirror

200

-200

[nm]

Mechanical Probe System Comparing with interferometer

• The small scale structure (centrosymmetric pattern) with amplitude of 50 nm is successfully detected

Interferometer

Test the Mirror

This work

New data reduction idea

• Multi continuous data generally conflict at overlap region.

• This problem can be removed efficiently and reliably by an idea that recognize the data as an elastic body. from JAXA

Example Scanning data of flat surface

Scanning path Actual data analyzed by current algorithm

by this algorithm

Predecessor well know nature…

Salvage the embedded information

Current techniques

Spatial filter or data binning techniques lost some information but this technique keep them

This techniques

Supporting mechanics

・SHWFS ・Phase Camera

Component of Segment Control System

Edge Sensor

Processor

Supporting mechanics

Segment

Segment

Actuator

Actuator

Kinematic Support for Segment

Actuator connected

Supporting point ×9

Segment

Segment Mirror

Flexure Pivot

Axial rod ×9 (Flexure)

• Segment mirror is supported by multi points in such a way that the segment floats without over constraint.

• Tip-tilt and piston of the segment are actuated via

the three pivots.

Actuator ×3

Segment Technics

Segment Techniques Supporting Structure

Deformation @ 0 deg RMS = 30 nm, P-V = 150 nm

1

10

100

1000

1 10 100 1000

Fig

ure

erro

r rm

s [n

m]

Separation[mm]

Deformation @ 90 deg RMS = 12 nm, P-V = 81 nm

Red：Requirement Blue：Support

SR0.76@1.0um SR0.58@0.7um

SR0.97@3.0um SR0.93@2.0um

Simulated SR considering the actual figure error of segments and supporting system

Segment Technics

Segment Techniques Edge Sensor

Modified DS2001

Requirement Resolution (RMS nm) < 10 Stability (P-V nm/10hr) 50 Linearity > 90% Sample rate Hz > 10 Range mm 1

13 hr

30 nm

Result under temperature changes of 5 degree

Segment Technics

Warping Harness

Simulation

Result obtained by CGH interferometer

Segment Mirror

Warping harness provides torque on the flexure pivot in order to • reduce the figure error of low order • correct the positioning error of the segment on the

mount(power and astigmatism) • correct the seasonal distortion

Segment Technics

Actuator

Lever (Flexure pivot)

output 1/30

Actuator

Decelerator

Input at actuator (μm)

Ou

tpu

t (

μm

)

Time (second)

Ou

tpu

t (μ

m)

Reverse motion test

Segment Technics

11/13

Feedback OFF

Actuator

Feedback ON

Put a load on and off the segment

Time (second)

Dis

pla

cem

ent

(nm

) Segment Technics

Processor

Optimized Configuration of Edge Sensors

A part of the result of control stiffness of the segment system

Cross section of the Segment and Edge Sensor Arrangement

Segment Technics

Lightweight Structure

• Truss structure

• Large arc rails for elevation bearing

• Homologous deformation optimized by genetic algorithm

Moving mass around elevation ：8 ton (4 ton optics) 1/5 of conventional telescope

Truss Structure

• The telescope tube consists of truss structure only

• Advantages

• Light but stiff

• Small cross section and low air drag

• Low heat capacity

• Large surface area and low heat inertia

Back view of primary mirror

Lightweight Structure

Large Arc rails

• The primary mirror is directly supported by large elevation rings without center section and mirror cell

center section

cell

This mount Conventional mount

In conventional mount ,because the center section and cell are supported by its periphery, bending moments load on them

Conventional radio telescope mount

Lightweight Structure

Homologous Deformation

• Serrurier Truss for keeping the optical alignment between the primary and secondary mirrors

– similar but more primitive idea to homologous deformation utilized in radio antennae

primary Secondary

Optical axis

Lightweight Structure

Kunda Masashi @ 夏ゼミ

Parent

88.51 kg

1st Generation

84.14 kg

3rd Generation

82.71 kg

10th Generation

77.52 kg

18th Generation

76.22 kg

Genetic Algorithm (GA) for lightweight and homologous deformation

Lightweight Structure

GA is a way to optimize a subject which has multi conflict object. In GA, a model devolves like a evolution of life by using Selection, Mutation, & Crossover

Cantilever example

1 tf

4 tf

Genetic Algorithm for lightweight and homologous deformation

Lightweight Structure

Requirement in homologous performance (El. 88～20 deg) • nodes for primary mirror in normal <0.1 mm • nodes for secondary mirror in lateral <2mm→0.4 mm • nodes for tertiary mirror in normal <0.05 mm Variable • Position of node (deleting is possible) • Cross section of straight member (deleting is possible) Material is selected from JIS member only Rate of crossover 0.8 Rate of Mutation 0.01

進化後のモデル

ホモ

ロガ

ス変

形(m

m）

重量（ton）

仕様範囲

Genetic Algorithm for lightweight and homologous deformation

First model

Final model

Lightweight Structure

初期解 最適解の一例

Acceptable deformation

0% 200%

Lightweight Structure

Genetic Algorithm for lightweight and homologous deformation

Homologous Deformation

• Dish must keep its shape under dead loads to satisfy optical performance.

Fixed elevation Active Support Rigid Structure Homologous Deformation

Homologous Deformation

Classical method for Homologous Deformation

• Element for Optimization – Objects: Homology of selected points 𝒏 on the

reflector • Sufficient 𝑛 must be selected, 𝑛 ∝ 𝐷2/𝜆2

• Weight and stiffness are not primary

– Design parameters: Degree of freedom of the model 𝑵

– Formulation: Stiffness matrix 𝐾 of the model and Newton method on the derivative of 𝐾−1

– Constraints: Geometry of the first model is fixed

𝒏

𝑁 > 𝑛

Homologous Deformation

Discussion Panel shape: Hexagon or Annular

• Hexagon – more efficient in process – mechanically stiffer (wider angle

of 120 deg at the corner) – more robust for segment control

system – identical supporting system for

all segments – easy to design the back structure

• Annular – less degradation of image due to

the diffraction – smaller number of the spare

segments

Dark area: waste region under rotary motion processing

Annular segment Hexagonal segment

Discussion Panel

• Panel – Material: Aluminum

– Support point: 3

– Thickness: 80 mm

– 30% Weight: 90 kgf • Solid 300 kg

– 30m dish: ～500 panels

• Our facility can deliver this size of panel in a few days per panel.

P-V=5 um, RMS=1.2 um (Solid)

1500

Discussion Configuration of Panel

All panels independently supported

Group panels supported by sub cells (Each sub cell supported by 3 points)

All panels connected to a single panel

Independent Group Single

Control type positioning positioning force

Sensor and Actuator

high precision long range

high precision short range/ Low precision Long range

Low precision

Homologous structure

yes no yes