Mail Delivery Subsystem wrote: > > The original message was received at Tue, 17 Jun 1997 16:10:50 +0200 > from smap@localhost > > ----- The following addresses had delivery problems ----- > <Marinus.Lugt@space-elec.dofn.de> (unrecoverable error) > > ----- Transcript of session follows ----- > 550 <Marinus.Lugt@space-elec.dofn.de>... User unknown > > ----- Original message follows ----- > Return-Path: <richas@idt.net> > Received: by space-elec.dofn.de (SMI-8.6/SMI-SVR4) > id QAA05236; Tue, 17 Jun 1997 16:10:50 +0200 > Received: from u2.farm.idt.net(169.132.8.11) by t1ws02 via smap (V1.3) > id sma005231; Tue Jun 17 16:10:35 1997 > Received: from richas.ios.com (ppp-66.ts-5.lax.idt.net [169.132.209.138]) > by u2.farm.idt.net (8.8.5/8.8.5) with SMTP id KAA24303 > for <Marinus.Lugt@space-elec.dofn.de>; Tue, 17 Jun 1997 10:07:47 -0400 (EDT) > Message-ID: <33A699F8.2D0A@idt.net> > Date: Tue, 17 Jun 1997 07:06:48 -0700 > From: Richard Schwartz <richas@IDT.NET> > Reply-To: richas@IDT.NET > Organization: Star Fleet Engineering > X-Mailer: Mozilla 3.0 (Win95; U) > MIME-Version: 1.0 > To: van der Lugt <Marinus.Lugt@space-elec.dofn.de> > Subject: Re: Formula for Diagonal Offset > References: <199706171304.PAA04753@space-elec.dofn.de> > Content-Type: text/plain; charset=us-ascii > Content-Transfer-Encoding: 7bit > content-length: 1331 > > > > r is the radius of the mirror. > > > f is the focal length > > > a = atan(r/f) > > > > > > offset =sma*(cse(135-a)-csc(45-a))/(csc(135-a)+csc(45-a)), > > > > > > where sma is the semi-major axis of the elliptical mirror > > > and offset is the distance from the center of the mirror surface > > > to the point where the optical axis intercept the mirror surface. > > > > > > For most of us, it is a real small number. > > > > > > > As I am not familiar with this expression or it's notations, a few questions. > > 1. cse = SIN (Sine) ? > > cse is a misprint. it should be csc, the co-secant. csc(x)=1/sin(x). > > > 2. csc = COS (Cosine) ? > > csc is co-secant. csc(x)=1/sin(x). > > > 3. sma = What is the semi-major axis ? Is this the length of the longest possible > > (straight) line that can be drawn on the secondary ?. > > No, it is the length from the center of the ellipse to the farthest > point on the ellipse. > > > If so, why is the size of the secondary important ? I would expect that only the > > distance between secondary and focal point would go into the equation. > > The above formula is based on a diagonal that just covers the light cone > for an image that is exactly in the center of the focal plane. So the > distance from the diagonal to the focal point is already figured into > the size of the diagonal. > > ASCII is a lousy way to convey math formulas!
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The original message was received at Tue, 17 Jun 1997 16:10:50 +0200 from smap@localhost ----- The following addresses had delivery problems ----- <Marinus.Lugt@space-elec.dofn.de> (unrecoverable error) ----- Transcript of session follows ----- 550 <Marinus.Lugt@space-elec.dofn.de>... User unknown ----- Original message follows ----- Return-Path: <richas@idt.net> Received: by space-elec.dofn.de (SMI-8.6/SMI-SVR4) id QAA05236; Tue, 17 Jun 1997 16:10:50 +0200 Received: from u2.farm.idt.net(169.132.8.11) by t1ws02 via smap (V1.3) id sma005231; Tue Jun 17 16:10:35 1997 Received: from richas.ios.com (ppp-66.ts-5.lax.idt.net [169.132.209.138]) by u2.farm.idt.net (8.8.5/8.8.5) with SMTP id KAA24303 for <Marinus.Lugt@space-elec.dofn.de>; Tue, 17 Jun 1997 10:07:47 -0400 (EDT) Message-ID: <33A699F8.2D0A@idt.net> Date: Tue, 17 Jun 1997 07:06:48 -0700 From: Richard Schwartz <richas@IDT.NET> Reply-To: richas@IDT.NET Organization: Star Fleet Engineering X-Mailer: Mozilla 3.0 (Win95; U) MIME-Version: 1.0 To: van der Lugt <Marinus.Lugt@space-elec.dofn.de> Subject: Re: Formula for Diagonal Offset References: <199706171304.PAA04753@space-elec.dofn.de> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit content-length: 1331 > > r is the radius of the mirror. > > f is the focal length > > a = atan(r/f) > > > > offset =sma*(cse(135-a)-csc(45-a))/(csc(135-a)+csc(45-a)), > > > > where sma is the semi-major axis of the elliptical mirror > > and offset is the distance from the center of the mirror surface > > to the point where the optical axis intercept the mirror surface. > > > > For most of us, it is a real small number. > > > > As I am not familiar with this expression or it's notations, a few questions. > 1. cse = SIN (Sine) ? cse is a misprint. it should be csc, the co-secant. csc(x)=1/sin(x). > 2. csc = COS (Cosine) ? csc is co-secant. csc(x)=1/sin(x). > 3. sma = What is the semi-major axis ? Is this the length of the longest possible > (straight) line that can be drawn on the secondary ?. No, it is the length from the center of the ellipse to the farthest point on the ellipse. > If so, why is the size of the secondary important ? I would expect that only the > distance between secondary and focal point would go into the equation. The above formula is based on a diagonal that just covers the light cone for an image that is exactly in the center of the focal plane. So the distance from the diagonal to the focal point is already figured into the size of the diagonal. ASCII is a lousy way to convey math formulas!
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