ó šßÈ[c@`sndZddlmZmZmZmZddlZddlm Z ddl m Z ddl m Z ddl m Z dd lmZdd l mZdd lmZd d dddddddddddddgZd„Zd„Zd„Zd„Zdd„Zd „Zd!„Zd"„Zd#„Zd$„Zd%„Z d&„Z!d'„Z"d(„Z#d)„Z$d*„Z%dS(+u-A set of standard astronomical equivalencies.i(tabsolute_importtdivisiontprint_functiontunicode_literalsNi(tsii(tcgs(t astrophys(tunits(tdimensionless_unscaled(t UnitsErroruparallaxuspectraluspectral_densityu doppler_radioudoppler_opticaludoppler_relativisticu mass_energyubrightness_temperatureudimensionless_anglesu logarithmicu temperatureutemperature_energyumolar_mass_amuu pixel_scaleu plate_scalecC`stjdfgS(uAllow angles to be equivalent to dimensionless (with 1 rad = 1 m/m = 1). It is special compared to other equivalency pairs in that it allows this independent of the power to which the angle is raised, and independent of whether it is part of a more complicated unit. N(RtradiantNone(((s:lib/python2.7/site-packages/astropy/units/equivalencies.pytdimensionless_anglesscC`sttjtjd„fgS(uBAllow logarithmic units to be converted to dimensionless fractionscS`sd|S(Ng$@((tx((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyt(s(Rtfunction_unitstdextnptlog10(((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyt logarithmic$s cC`stjtjd„fgS(uq Returns a list of equivalence pairs that handle the conversion between parallax angle and distance. cS`sd|S(Ngð?((R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyR2s(Rt arcsecondRtparsec(((s:lib/python2.7/site-packages/astropy/units/equivalencies.pytparallax,sc`sdtjjtjj‰dtj‰tjd}tjtj}tjtj d„ftjtj ‡fd†ftj tj d„d„ftj|d„ftj |d„d „ftj |‡fd †‡fd †f||‡fd †‡fd †ftj|‡fd†ftj |‡fd†‡fd†ftj |‡‡fd†‡‡fd†fg S(u« Returns a list of equivalence pairs that handle spectral wavelength, wave number, frequency, and energy equivalences. Allows conversions between wavelength units, wave number units, frequency units, and energy units as they relate to light. There are two types of wave number: * spectroscopic - :math:`1 / \lambda` (per meter) * angular - :math:`2 \pi / \lambda` (radian per meter) g@iÿÿÿÿcS`stjj|S(N(t_sitctvalue(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRJsc`sˆ|S(N((R (thc(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRKscS`stjj|S(N(RthR(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRLscS`s|tjjS(N(RRR(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRLscS`sd|S(Ngð?((R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRMscS`s|tjjS(N(RRR(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRNscS`stjj|S(N(RRR(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyROsc`s|ˆS(N((R (R(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRPsc`sˆ|S(N((R (R(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRPsc`s|ˆS(N((R (ttwo_pi(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRQsc`s|ˆS(N((R (R(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRQsc`sˆ|S(N((R (R(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRRsc`sˆ|tjjS(N(RRR(R (R(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRSsc`stjj|ˆS(N(RRR(R (R(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRTsc`s |ˆˆS(N((R (RR(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRUsc`s ˆ|ˆS(N((R (RR(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRUs( RRRRRtpiRtmR tHztJ(t inv_m_spect inv_m_ang((RRs:lib/python2.7/site-packages/astropy/units/equivalencies.pytspectral6s    $!c-`sáddlm}tˆ|ƒrG|dkr:tdƒ‚n|ˆ‰ntjjtj tj ƒ‰tj j j ‰ˆˆ‰t jtjtjdtj }t jtjtjdtj }t jtjdtj }|}tjtjdtj tj }tjtjdtj tj}t jtj tj} t jtj tj} t jtj } | } tjtj tj } tjtj tj}‡‡fd†}‡‡fd†}‡fd†}‡fd†}‡fd †}‡fd †}‡‡fd †}‡‡fd †}‡‡fd †}‡‡fd†}‡‡fd†}‡‡fd†}|}|}‡‡‡fd†}‡‡‡fd†}|}|} |}!|}"|}#|}$|}%|}&|}'|}(|})|}*|}+|},||||f||||f||||f||||f||||f||||f||||f||||f| | ||f| | || f| | |!|"f| | |#|$f| | |%|&f| ||'|(f|| |)|*f|| |+|,fgS(u  Returns a list of equivalence pairs that handle spectral density with regard to wavelength and frequency. Parameters ---------- wav : `~astropy.units.Quantity` `~astropy.units.Quantity` associated with values being converted (e.g., wavelength or frequency). Notes ----- The ``factor`` argument is left for backward-compatibility with the syntax ``spectral_density(unit, factor)`` but users are encouraged to use ``spectral_density(factor * unit)`` instead. i(tUnitBaseu7If `wav` is specified as a unit, `factor` should be setic`s"|ˆjtjtƒƒdˆS(Ni(tto_valueRtAAR#(R (tc_Apstwav(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyt converter‡sc`s"|ˆjtjtƒƒdˆS(Ni(R%RR&R#(R (R'R((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyt iconverterŠsc`s|ˆjtjtƒƒS(N(R%RRR#(R (R((s:lib/python2.7/site-packages/astropy/units/equivalencies.pytconverter_f_nu_to_nu_f_nusc`s|ˆjtjtƒƒS(N(R%RRR#(R (R((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyticonverter_f_nu_to_nu_f_nusc`s|ˆjtjtƒƒS(N(R%RR&R#(R (R((s:lib/python2.7/site-packages/astropy/units/equivalencies.pytconverter_f_la_to_la_f_la“sc`s|ˆjtjtƒƒS(N(R%RR&R#(R (R((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyticonverter_f_la_to_la_f_la–sc`sˆ|ˆjtjtƒƒS(N(R%RR&R#(R (RR((s:lib/python2.7/site-packages/astropy/units/equivalencies.pytconverter_phot_f_la_to_f_la™sc`s|ˆjtjtƒƒˆS(N(R%RR&R#(R (RR((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyticonverter_phot_f_la_to_f_laœsc`sˆ|ˆjtjtƒƒS(N(R%RR&R#(R (th_cgsR((s:lib/python2.7/site-packages/astropy/units/equivalencies.pytconverter_phot_f_la_to_f_nuŸsc`s|ˆjtjtƒƒˆS(N(R%RR&R#(R (R1R((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyticonverter_phot_f_la_to_f_nu¢sc`s"|ˆjtjtƒƒdˆS(Ni(R%RR&R#(R (R'R((s:lib/python2.7/site-packages/astropy/units/equivalencies.pytconverter_phot_f_la_phot_f_nu¥sc`s"ˆ|ˆjtjtƒƒdS(Ni(R%RR&R#(R (R'R((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyticonverter_phot_f_la_phot_f_nu¨sc`s&|ˆˆˆjtjtƒƒdS(Ni(R%RR&R#(R (R'RR((s:lib/python2.7/site-packages/astropy/units/equivalencies.pytconverter_phot_f_nu_to_f_la®sc`s&|ˆjtjtƒƒdˆˆS(Ni(R%RR&R#(R (R'RR((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyticonverter_phot_f_nu_to_f_la±sN(tcoreR$t isinstanceR t ValueErrorRRR%RR&tsRRRtergtangstromtcmRRtphoton(-R(tfactorR$tf_latf_nutnu_f_nutla_f_lat phot_f_lat phot_f_nutL_nutL_latnu_L_nutla_L_lat phot_L_lat phot_L_nuR)R*R+R,R-R.R/R0R2R3R4R5tconverter_phot_f_nu_to_f_nuticonverter_phot_f_nu_to_f_nuR6R7tconverter_L_nu_to_nu_L_nuticonverter_L_nu_to_nu_L_nutconverter_L_la_to_la_L_laticonverter_L_la_to_la_L_latconverter_phot_L_la_to_L_laticonverter_phot_L_la_to_L_latconverter_phot_L_la_to_L_nuticonverter_phot_L_la_to_L_nutconverter_phot_L_la_phot_L_nuticonverter_phot_L_la_phot_L_nutconverter_phot_L_nu_to_L_nuticonverter_phot_L_nu_to_L_nutconverter_phot_L_nu_to_L_laticonverter_phot_L_nu_to_L_la((R'R1RR(s:lib/python2.7/site-packages/astropy/units/equivalencies.pytspectral_densityYs†    """"c`sàtˆƒtjjdƒ‰‡‡fd†}‡‡fd†}‡‡fd†}‡‡fd†}‡‡fd†}‡‡fd†}tjtjtj||ftjtjtj||ftj tjtj||fgS(u« Return the equivalency pairs for the radio convention for velocity. The radio convention for the relation between velocity and frequency is: :math:`V = c \frac{f_0 - f}{f_0} ; f(V) = f_0 ( 1 - V/c )` Parameters ---------- rest : `~astropy.units.Quantity` Any quantity supported by the standard spectral equivalencies (wavelength, energy, frequency, wave number). References ---------- `NRAO site defining the conventions `_ Examples -------- >>> import astropy.units as u >>> CO_restfreq = 115.27120*u.GHz # rest frequency of 12 CO 1-0 in GHz >>> radio_CO_equiv = u.doppler_radio(CO_restfreq) >>> measured_freq = 115.2832*u.GHz >>> radio_velocity = measured_freq.to(u.km/u.s, equivalencies=radio_CO_equiv) >>> radio_velocity # doctest: +FLOAT_CMP ukm/sc`s+ˆjtjdtƒƒ}|||ˆS(Nt equivalencies(R%RRR#(R trestfreq(tckmstrest(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyt to_vel_freqüsc`s1ˆjtjdtƒƒ}|ˆ}|d|S(NR^i(R%RRR#(R R_tvoverc(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyt from_vel_freqs c`s(ˆjtjtƒƒ}|||ˆS(N(R%RR&R#(R trestwav(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyt to_vel_wavsc`s(ˆjtjtƒƒ}|ˆˆ|S(N(R%RR&R#(R Re(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyt from_vel_wav sc`s+ˆjtjdtƒƒ}|||ˆS(NR^(R%RteVR#(R tresten(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyt to_vel_en sc`s1ˆjtjdtƒƒ}|ˆ}|d|S(NR^i(R%RRhR#(R RiRc(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyt from_vel_ens ( tassert_is_spectral_unitRRR%RRtkmR;R&Rh(RaRbRdRfRgRjRk((R`Ras:lib/python2.7/site-packages/astropy/units/equivalencies.pyt doppler_radioÛs c`sàtˆƒtjjdƒ‰‡‡fd†}‡‡fd†}‡‡fd†}‡‡fd†}‡‡fd†}‡‡fd†}tjtjtj||ftjtjtj||ftj tjtj||fgS(u½ Return the equivalency pairs for the optical convention for velocity. The optical convention for the relation between velocity and frequency is: :math:`V = c \frac{f_0 - f}{f } ; f(V) = f_0 ( 1 + V/c )^{-1}` Parameters ---------- rest : `~astropy.units.Quantity` Any quantity supported by the standard spectral equivalencies (wavelength, energy, frequency, wave number). References ---------- `NRAO site defining the conventions `_ Examples -------- >>> import astropy.units as u >>> CO_restfreq = 115.27120*u.GHz # rest frequency of 12 CO 1-0 in GHz >>> optical_CO_equiv = u.doppler_optical(CO_restfreq) >>> measured_freq = 115.2832*u.GHz >>> optical_velocity = measured_freq.to(u.km/u.s, equivalencies=optical_CO_equiv) >>> optical_velocity # doctest: +FLOAT_CMP ukm/sc`s+ˆjtjdtƒƒ}ˆ|||S(NR^(R%RRR#(R R_(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRb=sc`s1ˆjtjdtƒƒ}|ˆ}|d|S(NR^i(R%RRR#(R R_Rc(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRdAs c`s(ˆjtjtƒƒ}ˆ||dS(Ni(R%RR&R#(R Re(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRfFsc`s.ˆjtjtƒƒ}|ˆ}|d|S(Ni(R%RR&R#(R ReRc(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRgJs c`s+ˆjtjdtƒƒ}ˆ|||S(NR^(R%RRhR#(R Ri(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRjOsc`s1ˆjtjdtƒƒ}|ˆ}|d|S(NR^i(R%RRhR#(R RiRc(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRkSs ( RlRRR%RRRmR;R&Rh(RaRbRdRfRgRjRk((R`Ras:lib/python2.7/site-packages/astropy/units/equivalencies.pytdoppler_opticals c`sàtˆƒtjjdƒ‰‡‡fd†}‡‡fd†}‡‡fd†}‡‡fd†}‡‡fd†}‡‡fd†}tjtjtj||ftjtjtj||ftj tjtj||fgS(u· Return the equivalency pairs for the relativistic convention for velocity. The full relativistic convention for the relation between velocity and frequency is: :math:`V = c \frac{f_0^2 - f^2}{f_0^2 + f^2} ; f(V) = f_0 \frac{\left(1 - (V/c)^2\right)^{1/2}}{(1+V/c)}` Parameters ---------- rest : `~astropy.units.Quantity` Any quantity supported by the standard spectral equivalencies (wavelength, energy, frequency, wave number). References ---------- `NRAO site defining the conventions `_ Examples -------- >>> import astropy.units as u >>> CO_restfreq = 115.27120*u.GHz # rest frequency of 12 CO 1-0 in GHz >>> relativistic_CO_equiv = u.doppler_relativistic(CO_restfreq) >>> measured_freq = 115.2832*u.GHz >>> relativistic_velocity = measured_freq.to(u.km/u.s, equivalencies=relativistic_CO_equiv) >>> relativistic_velocity # doctest: +FLOAT_CMP >>> measured_velocity = 1250 * u.km/u.s >>> relativistic_frequency = measured_velocity.to(u.GHz, equivalencies=relativistic_CO_equiv) >>> relativistic_frequency # doctest: +FLOAT_CMP >>> relativistic_wavelength = measured_velocity.to(u.mm, equivalencies=relativistic_CO_equiv) >>> relativistic_wavelength # doctest: +FLOAT_CMP ukm/sc`s?ˆjtjdtƒƒ}|d|d|d|dˆS(NR^i(R%RRR#(R R_(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRb†sc`s=ˆjtjdtƒƒ}|ˆ}|d|d|dS(NR^igà?(R%RRR#(R R_Rc(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRdŠs c`s<ˆjtjtƒƒ}|d|d|d|dˆS(Ni(R%RR&R#(R Re(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRfsc`s:ˆjtjtƒƒ}|ˆ}|d|d|dS(Nigà?(R%RR&R#(R ReRc(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRg“s c`s<ˆjtjtƒƒ}|d|d|d|dˆS(Ni(R%RRhR#(R Ri(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRj˜sc`s:ˆjtjtƒƒ}|ˆ}|d|d|dS(Nigà?(R%RRhR#(R RiRc(R`Ra(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRkœs ( RlRRR%RRRmR;R&Rh(RaRbRdRfRgRjRk((R`Ras:lib/python2.7/site-packages/astropy/units/equivalencies.pytdoppler_relativistic^s$ cC`stjtjtjfgS(u= Returns the equivalence between amu and molar mass. (RtgtmolRtu(((s:lib/python2.7/site-packages/astropy/units/equivalencies.pytmolar_mass_amu§scC`sªtjtjd„d„ftjtjdtjtjdd„d„ftjtjdtjtjdd„d„ftjtjtjtjd „d „fgS( ue Returns a list of equivalence pairs that handle the conversion between mass and energy. cS`s|tjjdS(Ni(RRR(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyR¶scS`s|tjjdS(Ni(RRR(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyR·sicS`s|tjjdS(Ni(RRR(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyR¹scS`s|tjjdS(Ni(RRR(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRºsicS`s|tjjdS(Ni(RRR(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyR¼scS`s|tjjdS(Ni(RRR(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyR½scS`s|tjjdS(Ni(RRR(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyR¾scS`s|tjjdS(Ni(RRR(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyR¿s(RtkgR RR;(((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyt mass_energy°s " "  c`sg|jtjƒ‰|jtjtƒƒ‰‡‡fd†}‡‡fd†}tjtj||fgS(u Defines the conversion between Jy/beam and "brightness temperature", :math:`T_B`, in Kelvins. The brightness temperature is a unit very commonly used in radio astronomy. See, e.g., "Tools of Radio Astronomy" (Wilson 2009) eqn 8.16 and eqn 8.19 (these pages are available on `google books `__). :math:`T_B \equiv S_\nu / \left(2 k \nu^2 / c^2 \right)` However, the beam area is essential for this computation: the brightness temperature is inversely proportional to the beam area Parameters ---------- beam_area : Beam Area equivalent Beam area in angular units, i.e. steradian equivalent disp : `~astropy.units.Quantity` with spectral units The observed `spectral` equivalent `~astropy.units.Unit` (e.g., frequency or wavelength) Examples -------- Arecibo C-band beam:: >>> import numpy as np >>> from astropy import units as u >>> beam_sigma = 50*u.arcsec >>> beam_area = 2*np.pi*(beam_sigma)**2 >>> freq = 5*u.GHz >>> equiv = u.brightness_temperature(beam_area, freq) >>> u.Jy.to(u.K, equivalencies=equiv) # doctest: +FLOAT_CMP 3.526294429423223 >>> (1*u.Jy).to(u.K, equivalencies=equiv) # doctest: +FLOAT_CMP VLA synthetic beam:: >>> bmaj = 15*u.arcsec >>> bmin = 15*u.arcsec >>> fwhm_to_sigma = 1./(8*np.log(2))**0.5 >>> beam_area = 2.*np.pi*(bmaj*bmin*fwhm_to_sigma**2) >>> freq = 5*u.GHz >>> equiv = u.brightness_temperature(beam_area, freq) >>> u.Jy.to(u.K, equivalencies=equiv) # doctest: +FLOAT_CMP 217.2658703625732 c`s?dtjtjˆdtjdjtjƒ}|ˆ|S(Ni(Rtk_BRtKRR%RtJy(tx_jybmR@(tbeamtnu(s:lib/python2.7/site-packages/astropy/units/equivalencies.pytconvert_Jy_to_Kös3c`s?tjdtjˆdtjdjtjƒ}|ˆ|S(Ni(RRyRRwRR%RRx(tx_KR@(R{R|(s:lib/python2.7/site-packages/astropy/units/equivalencies.pytconvert_K_to_Jyús3( R%RtsrttotGHzR#RRyRx(t beam_areatdispR}R((R{R|s:lib/python2.7/site-packages/astropy/units/equivalencies.pytbrightness_temperatureÃs 0cC`s_ddlm}tjtjd„d„ftj|d„d„ftj|d„d„fgS( uˆConvert between Kelvin, Celsius, and Fahrenheit here because Unit and CompositeUnit cannot do addition or subtraction properly. i(tdeg_FcS`s|dS(Ngfffffq@((R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRscS`s|dS(Ngfffffq@((R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRscS`s |ddS(NgÍÌÌÌÌÌü?g@@((R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRscS`s |ddS(Ng@@gÍÌÌÌÌÌü?((R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRscS`s|dddS(Ngfffffq@gÍÌÌÌÌÌü?g@@((R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyR scS`s|dddS(Ng@@gÍÌÌÌÌÌü?gfffffq@((R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyR s(timperialR†RRxtdeg_C(R†((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyt temperatures cC`stjtjd„d„fgS(u;Convert between Kelvin and keV(eV) to an equivalent amount.cS`s|tjjtjjS(N(RteRRw(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRscS`s|tjjtjjS(N(RRŠRRw(R ((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRs(RRxRh(((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyttemperature_energy scC`sFy|jtjtƒƒWn%ttfk rA}tdƒ‚nXdS(NuRThe 'rest' value must be a spectral equivalent (frequency, wavelength, or energy).(RRRR#tAttributeErrorR (Rtex((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRlsc`s«|jjtjtjƒr8|jtjtjƒ‰nH|jjtjtjƒrtd|jtjtjƒ‰n tdƒ‚tjtj‡fd†‡fd†fgS(u Convert between pixel distances (in units of ``pix``) and angular units, given a particular ``pixscale``. Parameters ---------- pixscale : `~astropy.units.Quantity` The pixel scale either in units of angle/pixel or pixel/angle. iu5The pixel scale must be in angle/pixel or pixel/anglec`s|ˆS(N((tpx(t pixscale_val(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyR.sc`s|ˆS(N((trad(R(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyR.s( tunitt is_equivalentRtarcsecRtpixR%R R (tpixscale((Rs:lib/python2.7/site-packages/astropy/units/equivalencies.pyt pixel_scales   c`s«|jjtjtjƒr8|jtjtjƒ‰nH|jjtjtjƒrtd|jtjtjƒ‰n tdƒ‚tjtj‡fd†‡fd†fgS(u! Convert between lengths (to be interpreted as lengths in the focal plane) and angular units with a specified ``platescale``. Parameters ---------- platescale : `~astropy.units.Quantity` The pixel scale either in units of distance/pixel or distance/angle. iu;The pixel scale must be in angle/distance or distance/anglec`s|ˆS(N((td(tplatescale_val(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRCsc`s|ˆS(N((R(R˜(s:lib/python2.7/site-packages/astropy/units/equivalencies.pyRCs(R‘R’RR“RR%R R (t platescale((R˜s:lib/python2.7/site-packages/astropy/units/equivalencies.pyt plate_scale1s   (&t__doc__t __future__RRRRtnumpyRt constantsRRtRRtfunctionRRRR8R t__all__R RRR#R R]RnRoRpRtRvR…R‰R‹RlR–Rš(((s:lib/python2.7/site-packages/astropy/units/equivalencies.pyts<"       # ‚ A B I  >