explanation      blue bibcodes open ADS page with paths to full text
Author name code: brandt
ADS astronomy entries on 2022-09-14
author:"Brandt, Peter N." AND aff:"Freiburg" 

---------------------------------------------------------
Title: Do Long-Lived Features Really Exist in the Solar
    Photosphere? II. Contrast of Time-Averaged Granulation Images
Authors: Brandt, P. N.; Getling, A. V.
2008SoPh..249..307B    Altcode: 2008arXiv0802.0204B; 2008SoPh..tmp...64B
  The decrease in the rms contrast of time-averaged images with the
  averaging time is compared between four data sets: (1) a series of
  solar granulation images recorded at La Palma in 1993, (2) a series
  of artificial granulation images obtained in numerical simulations
  by Rieutord et al. (Nuovo Cimento25, 523, 2002), (3) a similar
  series computed by Steffen and his colleagues (see Wedemeyer et
  al. in Astron. Astrophys.44, 1121, 2004), (4) a random field with
  some parameters typical of the granulation, constructed by Rast
  (Astron. Astrophys.392, L13, 2002). In addition, (5) a sequence of
  images was obtained from real granulation images by using a temporal
  and spatial shuffling procedure, and the contrast of the average of n
  images from this sequence as a function of n is analysed. The series
  (1) of real granulation images exhibits a considerably slower contrast
  decrease than do both the series (3) of simulated granulation images
  and the series (4) of random fields. Starting from some relatively
  short averaging times t, the behaviour of the contrast in series (3)
  and (4) resembles the t<SUP>−1/2</SUP> statistical law, whereas
  the shuffled series (5) obeys the n<SUP>−1/2</SUP> law from n=2
  on. Series (2) demonstrates a peculiarly slow decline of contrast,
  which could be attributed to particular properties of the boundary
  conditions used in the simulations. Comparisons between the analysed
  contrast-variation laws indicate quite definitely that the brightness
  field of solar granulation contains a long-lived component, which could
  be associated with locally persistent dark intergranular holes and/or
  with the presence of quasi-regular structures. The suggestion that the
  random field (4) successfully reproduces the contrast-variation law
  for the real granulation (Rast in Astron. Astrophys.392, L13, 2002)
  can be dismissed.

---------------------------------------------------------
Title: Dynamics of solar mesogranulation
Authors: Leitzinger, M.; Brandt, P. N.; Hanslmeier, A.; Pötzi, W.;
   Hirzberger, J.
2005A&A...444..245L    Altcode:
  Using a 45.5-h time series of photospheric flow fields generated
  from a set of high-resolution continuum images (SOHO/MDI) we analyze
  the dynamics of solar mesogranule features. The series was prepared
  applying a local correlation tracking algorithm with a 4.8´´ FWHM
  window. By computing 1-h running means in time steps of 10 min we
  generate 267 averaged divergence maps that are segmented to obtain
  binary maps. A tracking algorithm determines lifetimes and barycenter
  coordinates of regions of positive divergence defined as mesogranules
  (MGs). If we analyze features of lifetimes ≥1 h and of areas ≥5
  Mm{<SUP>2</SUP> we find a mean drift velocity of 304 m s<SUP>-1</SUP>
  (with ± 1σ variation of 180 m s<SUP>-1</SUP>), a mean travel distance
  of 2.5 ± 1.8 Mm, a mean lifetime of 2.6 ± 1.8 h, and a 1/e decay time
  of 1.6 h for a total of 2022 MGs. The advective motion of MGs within
  supergranules is seen for 50 to 70% of the long-lived (≥4 h) MGs while
  the short-lived ones move irregularly. If only the long-lived MGs are
  further analyzed the drift velocities reduce to 207 m s<SUP>-1</SUP>
  and the travel distances increase to 4.1 Mm on average, which is an
  appreciable fraction of the supergranular radius. The results are
  largely independent of the divergence segmentation level.

---------------------------------------------------------
Title: Solar Site Survey for the Advanced Technology Solar
    Telescope. I. Analysis of the Seeing Data
Authors: Socas-Navarro, H.; Beckers, J.; Brandt, P.; Briggs, J.;
   Brown, T.; Brown, W.; Collados, M.; Denker, C.; Fletcher, S.; Hegwer,
   S.; Hill, F.; Horst, T.; Komsa, M.; Kuhn, J.; Lecinski, A.; Lin, H.;
   Oncley, S.; Penn, M.; Rimmele, T.; Streander, K.
2005PASP..117.1296S    Altcode: 2005astro.ph..8690S
  The site survey for the Advanced Technology Solar Telescope concluded
  recently after more than 2 years of data gathering and analysis. Six
  locations, including lake, island, and continental sites, were
  thoroughly probed for image quality and sky brightness. The present
  paper describes the analysis methodology employed to determine the
  height stratification of the atmospheric turbulence. This information
  is crucial, because daytime seeing is often very different between the
  actual telescope aperture (~30 m) and the ground. Two independent
  inversion codes have been developed to simultaneously analyze
  data from a scintillometer array and a solar differential image
  monitor. We show here the results of applying them to a sample subset
  of data from 2003 May that was used for testing. Both codes retrieve a
  similar seeing stratification through the height range of interest. A
  quantitative comparison between our analysis procedure and actual in
  situ measurements confirms the validity of the inversions. The sample
  data presented in this paper reveal a qualitatively different behavior
  for the lake sites (dominated by high-altitude seeing) and the rest
  (dominated by near-ground turbulence).

---------------------------------------------------------
Title: The ATST Site Survey
Authors: Hill, F.; Beckers, J.; Brandt, P.; Briggs, J. W.; Brown, T.;
   Brown, W.; Collados, M.; Denker, C.; Fletcher, S.; Hegwer, S.; Horst,
   T.; Komsa, M.; Kuhn, J.; Lecinski, A.; Lin, H.; Oncley, S.; Penn, M.;
   Radick, R.; Rimmele, T.; Socas-Navarro, H.; Soltau, D.; Streander, K.
2005AGUSMSP34A..04H    Altcode:
  The Advanced Technology Solar Telescope (ATST) will be the world's
  largest aperture solar telescope, and is being designed for high
  resolution, IR, and coronal research. It must be located at a site that
  maximizes the scientific return of this substantial investment. We
  present the instrumentation, analysis and results of the ATST site
  survey. Two instrumentation sets were deployed at each of six sites to
  measure seeing as a function of height, and sky brightness as a function
  of wavelength and off-limb position. Analysis software was developed
  to estimate the structure function Cn2 as a function of height near
  the ground, and the results were verified by comparison with in-situ
  measurements. Additional software was developed to estimate the sky
  brightness. The statistics of the conditions at the sites were corrected
  for observing habits and the annualized hours of specific observing
  conditions were estimated. These results were used to identify three
  excellent sites suitable to host the ATST: Haleakala, Big Bear and La
  Palma. Among them, Haleakala is proposed as the optimal location of
  the ATST, La Palma and Big Bear being viable alternative sites.

---------------------------------------------------------
Title: The first decades of JOSO -- the Joint Organization for
    Solar Observations
Authors: Brandt, Peter N.; Mattig, Wolfgang
2005AcHA...25..240B    Altcode:
  In 1969 a group of leading European solar physicists established
  the Joint Organization for Solar Observations (JOSO) with the aim to
  promote international cooperation and to find an outstanding site for a
  new European solar observatory. After an extensive site test finally in
  1979 they found excellent sites on the Canary Islands for the deployment
  of several national instruments in the framework of the newly founded
  Instituto de Astrofísica de Canarias. The well co-ordinated thriving
  international cooperation made the continuation of JOSO desirable
  even after the fulfilment of the originally planned goals. New fields
  of cooperation were found, in particular the ground-based support of
  the SOHO mission. After the fall of the “iron curtain” in 1989
  intensive collaboration with the Eastern-European institutes was
  initiated, and JOSO turned into an enterprise for broad scientific
  and technological exchange.

---------------------------------------------------------
Title: Families of fragmenting granules and their relation to meso-
    and supergranular flow fields
Authors: Roudier, Th.; Lignières, F.; Rieutord, M.; Brandt, P. N.;
   Malherbe, J. M.
2003A&A...409..299R    Altcode:
  3D analysis (x,y,t) of the granular intensity field (11-hour time
  sequence from the Swedish Vacuum Solar Telescope on La Palma, Canary
  Islands), demonstrates that a significant fraction of the granules in
  the photosphere are organized in the form of “Trees of Fragmenting
  Granules" (TFGs). A TFG consists of a family of repeatedly splitting
  granules, originating from a single granule at its beginning. A striking
  result is that TFGs can live much longer (up to 8 h) than individual
  granules (10 min). We find that 62% of the area covered by granules
  belongs to TFGs of a lifetime &gt;1.5 h. When averaged in time, such
  long-lived TFGs correspond to coherent diverging flows which may be
  identified as mesogranules. We also find a correlation between the
  network and the spatial distribution of TFGs.

---------------------------------------------------------
Title: Deriving effective sunspot temperatures from SOHO/VIRGO
    irradiance measurements.  A starspot modelling approach
Authors: Eker, Z.; Brandt, P. N.; Hanslmeier, A.; Otruba, W.;
   Wehrli, C.
2003A&A...404.1107E    Altcode:
  A method is developed to obtain mean effective sunspot temperatures
  from satellite irradiance deficits. Using a formalism derived from
  a star spot modelling approach, this method only requires accurate
  positions and areas of sunspots - but not intensities. The method
  is applied to SOHO/VIRGO spectral solar irradiance (SSI) at 402,
  500, and 862 nm as well as total solar irradiance (TSI) measured
  during the period 16 July to 17 August 1996, the disk passage of
  active region NOAA 7981. MDI full disk white-light images are used
  to extract sunspot positions and areas. First, using the spot pixels,
  which are identified on MDI images as I<SUB>s</SUB> &lt; 0.92, we find
  the mean effective temperature of NOAA 7981 to be =~ 300 K less than
  the local photospheric temperature. Because the area is dominated by
  penumbral pixels, the temperature is close to a value representing the
  penumbra. Second, separating umbral and penumbral pixels, we obtain a
  temperature difference of =~ 850 K for the umbra and of =~ 200 K for the
  penumbra. Finally, if a 5% binning of the spot intensities is applied,
  a temperature deficit of =~ 1000 K is found for the darkest regions
  of the spot. <P />Appendixes A, B are only available in electronic
  form at http://www.edpsciences.org

---------------------------------------------------------
Title: Recurrence of fragmenting granules and their relation to meso-
    and supergranular flow fields
Authors: Roudier, Th.; Lignières, F.; Rieutord, M.; Brandt, P. N.;
   Malherbe, J. -M.
2003EAS.....9..371R    Altcode:
  The 3D analysis (x, y, t) of the granulation intensity field (11-hour
  time sequence from Swedish Vacuum Solar Telescope on La Palma, Canary
  Islands), demonstrated that the granules in the phostosphere are
  organized in “Trees of Fragmenting Granules" (TFGs). A TFG consists of
  a family of repeatedly splitting granules, issued from one granule at
  its beginning. A striking result is that TFGs can live much longer (up
  to 8h10) than individual granules (10 mn). When averaged in time, such
  long-lived TFGs can be identified to the mesogranules. We also found
  a correlation between the network and the spatial distribution of TFGs.

---------------------------------------------------------
Title: Evolution and motions of small-scale photospheric structures
    near a large solar pore
Authors: Dorotovič, I.; Sobotka, M.; Brandt, P. N.; Simon, G. W.
2002A&A...387..665D    Altcode:
  The analysis of an 11-hour series of high resolution white light
  observations of a large pore in the sunspot group NOAA 7519, observed
  on 5 June 1993 at the Swedish Vacuum Solar Telescope, La Palma, Canary
  Islands, is described. We used a total of 1782 frames, with average
  time interval of 22 s. Special attention was paid to the evolution of a
  filamentary region attached to the pore, to horizontal motions around
  the pore, and to small-scale morphological changes. The filamentary
  region was observed to change its structure back and forth between
  penumbra-like filaments and elongated granules. A clockwise rotation
  of this region around the center of the pore was detected during the
  whole observing period. This rotation had angular velocities decreasing
  with time from 7.6<SUP>deg</SUP> h<SUP>-1</SUP> to 2.7<SUP>deg</SUP>
  h<SUP>-1</SUP>. Motions inside the filamentary region and around the
  pore, including penetrations of photospheric granules into the pore,
  were studied in detail using local correlation and feature tracking
  algorithms. It was found that the observed filamentary region,
  although having some typical penumbral features, was different from
  a normal penumbra.

---------------------------------------------------------
Title: Evolution of Filamentary Structures in and around a Large
    Solar Pore
Authors: Simon, G. W.; Dorotovič, I.; Sobotka, M.; Brandt, P. N.
2002AAS...200.3803S    Altcode: 2002BAAS...34..698S
  We have studied evolution of a filamentary region attached to a pore,
  horizontal motions around the pore, and small-scale morphological
  changes, using an 11-hour series of 1782 high resolution white-light
  images of a large pore in the sunspot group NOAA 7519, acquired on
  5 June 1993 at the Swedish Vacuum Solar Telescope, La Palma, Canary
  Islands. We find that the structure of the region between the large pore
  and an adjacent micropore was not always filamentary, but varied back
  and forth in time between a filamentary structure and a granular one. A
  clockwise rotation, at times exceeding 7 deg/h, of this filamentary
  region around the center of the pore, was observed during the whole
  run. Motions of fine structure around and within the pore were studied
  in detail using local correlation and feature tracking. We conclude
  that the filamentary region, while it had some typical penumbral
  characteristics, was different from a normal penumbra. This research has
  been funded by the USAF Research Lab, and by Emeritus Research Services.

---------------------------------------------------------
Title: Regular structures of the solar photosphere. (Persistence of
    the granular field and trenching in the brightness relief)
Authors: Getling, A. V.; Brandt, P. N.
2002A&A...382L...5G    Altcode:
  The simple procedure of time averaging, when applied to the
  photospheric brightness field, reveals quasi-regular structures of
  the photospheric and subphotospheric flows. We use an 8-h sub-set of
  the series of photospheric images obtained on 5 June 1993 with the
  Swedish Vacuum Solar Telescope, La Palma. First, the averaged images
  are far from completely smeared and contain a multitude of bright,
  granular-sized blotches even if the averaging period is as long as 8
  h. This suggests that granules prefer to originate at certain sites,
  where they emerge repeatedly, and the granular field demonstrates a
  sort of persistence for many hours. Second, the resulting patterns
  display relatively regular structures, which can be revealed only if
  the averaging period is sufficiently long (the optimum seems to lie
  between 2 and 3 h). The averaged brightness relief is “trenched”:
  it comprises systems of concentric rings and arcs as well as straight
  or slightly wavy lines and systems of parallel strips. The trenching
  patterns resemble the so-called target patterns observed in experiments
  on Rayleigh-Bénard convection. In addition, the brightness values
  at a local averaged-field maximum and at a nearby minimum exhibit a
  distinct tendency to vary in antiphase. Thus, a previously unknown
  type of self-organization is manifest in the solar atmosphere, and
  our findings support the suggestion that granules are associated with
  overheated blobs carried by the convective circulation.

---------------------------------------------------------
Title: Time-slice diagrams of solar granulation
Authors: Müller, D. A. N.; Steiner, O.; Schlichenmaier, R.; Brandt,
   P. N.
2001SoPh..203..211M    Altcode:
  From a series of 1400 white-light images of solar granulation spanning
  a time period of 8.2 hours, skeletal plots of time-slice diagrams are
  derived showing intergranular lane positions as a function of time. The
  diagrams permit to automatically track, classify, and relate 42 186
  granules. Recurrently fragmenting granules are found that survive
  by means of their descendants for more than 3 hours. Such long-lived
  active granules tend to have a mean spatial distance along the slice
  of about 10 Mm. This distance decreases with decreasing minimal
  required lifetime. Since active granules are expected to generate a
  steadily divergent flow over a long period of time, it is suggested
  to identify them as a source of the mesogranular flow. Deficiencies
  of the time-slice analysis are discussed. The relative frequency of
  different types of granules and the granule decay time as derived
  from the time-slice diagrams are compared with corresponding results
  of previous works.

---------------------------------------------------------
Title: Modeling VIRGO Spectral and Bolometric Irradiances with
    MDI Data
Authors: Steinegger, M.; Hanslmeier, A.; Otruba, W.; Brandt, P. N.;
   Eker, Z.; Wehrli, C.; Finsterle, W.
2001ASSL..259..283S    Altcode: 2001dysu.conf..283S
  The last solar activity minimum in 1996 was characterized by
  several periods without any sunspots or faculae visible on the solar
  disk. Between these extremely quiet intervals, from time to time
  a single active region emerged and developed. The passage of these
  individual active regions across the visible solar hemisphere was
  accompanied by a pronounced variation in the solar irradiance as
  observed by VIRGO onboard SOHO. Making use of photometric full-disk
  observations of the Sun obtained by MDI we try to reconstruct the
  temporal behaviour of the three spectral and the total irradiance
  channels measured by VIRGO by applying starspot modeling techniques. In
  this paper we mainly discuss possible error sources.

---------------------------------------------------------
Title: Computational Methods concerning the Solar Granulation
Authors: Pötzi, W.; Hanslmeier, A.; Brandt, P. N.
2001ASSL..259..223P    Altcode: 2001dysu.conf..223P
  In this paper an overview is given concerning the automatic detection
  of granules in long time series and the derivation of characteristic
  parameters.

---------------------------------------------------------
Title: Preliminary study of the evolution of solar magnetic structures
    and photospheric horizontal velocity fields
Authors: UeNo, S.; Kitai, R.; Ichimoto, K.; Sakurai, T.; Soltau, D.;
   Brandt, P. N.
2001AdSpR..26.1793U    Altcode:
  In October 1997, we made a coordinated observation of the solar
  photosphere and chromosphere at Hida observatory (Kyoto university,
  Japan) and at Teide observatory (Tenerife) over a 10 day. We obtained
  imaging data series continuously during 6 hr 45 min in G-band (4308 Å)
  observed with the Domeless Solar Telescope (DST) at Hida on 24th October
  (effective FOV; 96″×99″). Additionally, in this observation,
  we simultaneously observed image series of the chromosphere during
  the latter 4 hr 10 min in H α line center and H α ±0.6 Å. From
  these data set, we could detect that emerging flux tubes crossed
  the photosphere to the chromosphere and that 'convective collapse'
  phenomena appeared at the stage of the spot formation. Moreover,
  we confirmed that the lifetime of mesogranulation was about 4000 sec
  (70 min) from the temporal evolution of velocity patterns. We show
  here only a summary of these observations.

---------------------------------------------------------
Title: Coordinated MDI/TRACE/SVST Observations of Sunspots
Authors: Bush, R. I.; Shine, R. A.; Brandt, P.; Sobotka, M.;
   Scharmer, G.
2000SPD....31.0122B    Altcode: 2000BAAS...32R.804B
  During the first two weeks of June 1999, coordinated observations
  of sunspots were made by the MDI instrument on the SOHO spacecraft,
  the TRACE satellite and the Swedish Vacuum Solar Tower (SVST) at La
  Palma. The MDI instrument was operating in a "high resolution" mode
  and was obtaining 1.2 arc-second resolution magnetograms and 2.4
  arc-second resolution dopplergrams at a one minute cadence. TRACE
  observations were made in Fe IX/X 171 Angstroms and/or Fe XII 195
  Angstroms together with the 1600 Angstroms and continuum bands at a
  1.0 arc-second resolution. The SVST data consist of filtergrams taken
  with three 2Kx2K CCD cameras with about 0.4 arc-second resolution
  operating in frame selection mode. The first camera used a fixed G
  band (4305 Angstroms) filter, the second a fixed blue continuum filter
  (4507 Angstroms), and the third a narrow band tunable filter which was
  cycled through several positions in the Hα line and the 6302 Angstroms
  Fe ~I line. The goal of this investigation is to detail the evolution
  of stable sunspots in order to understand the detailed correlation of
  photospheric flows and magnetic features. The high time and spatial
  resolution of these measurements provides a unique opportunity to
  explore the interactions of plasma and magnetic field at the solar
  surface. This work was supported by NASA grant NAG5-3077 at Stanford
  and NASA contract NAS5-38099 at Lockheed Martin.

---------------------------------------------------------
Title: Small-scale topology of solar atmosphere dynamics. IV. On
    the relation of photospheric oscillations to meso-scale flows
Authors: Hoekzema, Nick M.; Brandt, Peter N.
2000A&A...353..389H    Altcode:
  We use a high quality five-hour sequence of images of the solar
  photosphere taken at the Swedish Solar Vacuum Telescope, La Palma,
  to study the relation of meso-scale divergence with the amplitudes of
  photospheric intensity oscillations. Meso-scale flows are determined by
  local correlation tracking of the granulation. Statistical evaluation
  of the co-location probability of regions with more than twice the
  average oscillation amplitude and regions with high or low meso-scale
  divergence shows that high amplitude regions are preferentially located
  in regions of negative divergence (convergence) and avoid meso-divergent
  regions. Additionally we confirm the increase of granule brightness
  in regions of positive divergence with the opposite effect in regions
  of convergence.

---------------------------------------------------------
Title: Fine structure in sunspots. III. Penumbral grains
Authors: Sobotka, M.; Brandt, P. N.; Simon, G. W.
1999A&A...348..621S    Altcode:
  The properties of penumbral grains (PGs) in a medium-size sunspot are
  studied from a 4.5 hour observation series acquired on 5 June 1993 at
  the Swedish Vacuum Solar Telescope, La Palma. The application of an
  image segmentation procedure and a feature tracking algorithm on a movie
  of 360 frames yields proper motions, intensities, and lifetimes for a
  set of 469 PGs. Almost 3/4 of the PGs move toward the umbra and more
  than 1/4 toward the photosphere. There appears to be a dividing line
  (DL) in the penumbra, approximately 0.7 of the distance from the umbra
  to the photosphere, such that most PGs outside this line move toward
  the photosphere, and those inside move toward the umbra. For inward
  moving PGs we find a typical proper motion speed of 0.4 km s(-1) and
  a median lifetime of 29 minutes, for outward moving ones 0.5 km s(-1)
  and 22 minutes. The average speed of inward moving PGs increases with
  distance from the umbra with a maximum near the DL. Outward moving
  PGs have maximum speed near the outer penumbral boundary. The measured
  instantaneous velocities of individual PGs show only partial agreement
  with theoretical model predictions. We find much shorter lifetimes than
  earlier authors, and no pronounced dependence of lifetime on position
  in the penumbra. We discuss possible reasons for the disagreement with
  previous results.

---------------------------------------------------------
Title: Shift-and-add reconstruction of solar granulation images
Authors: Baba, N.; Miura, N.; Sakurai, T.; Ichimoto, K.; Soltau, D.;
   Brandt, P.
1999SoPh..188...41B    Altcode:
  To restore an atmospherically degraded image of solar granulation the
  shift-and-add (SAA) method is applied to its specklegrams. It is the
  first time, to the best of our knowledge, that such a technique has
  been used for image reconstruction of solar granulation, a largely
  extended target. SAA, therefore, enables us to monitor restored images
  of solar granulation in a simple and fast way.

---------------------------------------------------------
Title: Resolution Improvement of Solar Images
Authors: Miura, Noriaki; Baba, Naoshi; Sakurai, Takashi; Ichimoto,
   Kiyoshi; Soltau, Dirk; Brandt, Peter
1999SoPh..187..347M    Altcode:
  A method for the improvement of resolution in an observed solar image
  is proposed. A blind deconvolution method is used for restoration of an
  atmospherically-degraded solar image, and a super-resolution method is
  applied to its restored image to improve the resolution. It is confirmed
  that a blind deconvolution process can restore fine structures that are
  blurred in an observed image, and that the super-resolution process
  can make a cutoff frequency in a blind-deconvolved image higher. A
  time series of super-resolved images of a sunspot observed with the
  70-cm Vacuum Tower Telescope at Teide Observatory is presented.

---------------------------------------------------------
Title: Modelling of Solar Irradiance Variations
Authors: Otruba, W.; Brandt, P. N.; Eker, Z.; Hanslmeier, A.;
   Steinegger, M.
1999ASSL..239..213O    Altcode: 1999msa..proc..213O
  A modelling of the sunspot deficit in solar irradiance measurements
  in 3 spectral wavelengths and the total flux as observed by the VIRGO
  experiment on SOHO has been performed for several periods of 1996 in
  a pixel-by-pixel manner using high resolution photoheliograms taken at
  Kanzelhöhe Observatory. The calculation of the irradiance contributions
  of the other features of active regions is in progress.

---------------------------------------------------------
Title: Some Properties of the Solar Granulation and Mesogranulation
Authors: Mühlmann, W.; Hanslmeier, A.; Brandt, P. N.
1999ASSL..239..223M    Altcode: 1999msa..proc..223M
  Based on a 8.7 hour time series of solar granulation images (Simon
  et al., 1994), of a spatial resolution mostly better than 400 km, we
  calculated some properties of granules, vorticity and divergence of
  the velocity fields and we tried to determine the mesogranular pattern
  by corks.

---------------------------------------------------------
Title: Small-scale topology of solar atmosphere
    dynamics. III. Granular persistence and photospheric wave amplitudes
Authors: Hoekzema, N. M.; Brandt, P. N.; Rutten, R. J.
1998A&A...333..322H    Altcode:
  We use a superb five-hour sequence of 900 solar images taken at La
  Palma to study long-duration persistence in the solar granulation,
  in the context of the long-lived “intergranular holes” discovered by
  \cite*{Roudier+others1997} %T AA: intergranular plumes + BP formation
  and the contention that these mark sites of convective downflow
  plumes. We develop a procedure to locate “persistency regions” that
  contain granular brightness maxima or minima over extended periods
  (up to 45 min), while allowing for lateral drifts due to horizontal
  flows. Statistical evaluation of the co-location probability for
  different pixel classes is first used to quantify the likelihood of
  long-term stationarity for different granular brightness classes and for
  the persistency regions, and then to evaluate the amount of preferential
  alignment, at different frequencies and time delays, between excessive
  Fourier modulation and granular brightness and persistence. The results
  support the existence of long-lived intergranular holes. There is large
  persistency difference between the brightest and the darkest features;
  some of the latter have location memories as long as two hours. In
  addition, the darkest intergranular features are found to be sites of
  enhanced Fourier modulation in the 3-min acoustic regime, improving
  earlier results through much higher statistical significance. However,
  the persistency regions containing intergranular holes do not seem
  to produce the excess acoustic emission that would be expected above
  downflow plumes.

---------------------------------------------------------
Title: On the Determination of the Quiet-Sun Center-to-Limb Variation
    in CA II K Spectroheliograms
Authors: Brandt, Peter N.; Steinegger, Michael
1998SoPh..177..287B    Altcode:
  We present a method for the determination of the center-to-limb
  variation (CLV) for Caii K spectroheliograms. It is based on the
  calculation of intensity histograms for rings of constant area. Using
  a simple cutoff criterion in the cumulative histograms, we are able
  to derive CLVs of the quiet Sun regardless of the solar activity
  level. Using an example from the literature, we show in which way
  different methods of normalization of the quiet-Sun CLV may affect
  the results.

---------------------------------------------------------
Title: Small-scale topology of solar atmosphere dynamics. I. Wave
    sources and wave diffraction
Authors: Hoekzema, N. M.; Rutten, R. J.; Brandt, P. N.; Shine, R. A.
1998A&A...329..276H    Altcode:
  We study the small-scale topology of dynamical phenomena in the
  quiet-sun internetwork atmosphere, using short-duration Fourier analysis
  of high-resolution filtergram sequences to obtain statistical estimates
  for the co-location probability of different fine-structure elements
  and wave modes. In this initial paper we concentrate on the topology
  of short-duration Fourier amplitude maps for the photosphere and the
  simultaneously observed overlying chromosphere. We find that these
  maps portray a complex mix of global modes and locally excited waves
  which necessitates a statistical approach. Various aspects including
  mesoscale patterning indicate the presence of subsurface wave sources
  and of subsurface wave diffraction by convective inhomogeneities.

---------------------------------------------------------
Title: Fine structure in sunspots. I. Sizes and lifetimes of
    umbral dots
Authors: Sobotka, Michal; Brandt, Peter N.; Simon, George W.
1997A&A...328..682S    Altcode:
  The analysis of a 4 1/2 hour series of high resolution white light
  observations of the umbra in a medium-size sunspot (NOAA 7519, observed
  on 5 June 1993 at the Swedish Vacuum Solar Telescope, La Palma) is
  described. An automatic identification and tracking algorithm was
  applied to umbral dots (UDs) observed in a destretched movie of 360
  frames. In total, 662 UDs were tracked and their filling factor, sizes,
  and lifetimes were measured. It was found that large (diameter &gt;
  0farcs 4) and long-lived (lifetime &gt; 10 minutes) UDs appear mostly
  in regions with enhanced umbral diffuse background intensity. UDs
  do not have a “typical” size. Their number rapidly increases with
  decreasing diameter down to the resolution limit. Similarly, UDs do
  not have a “typical” lifetime, and their number rapidly increases
  with decreasing lifetime. UDs with lifetimes below 10 minutes represent
  about 2/3 of the population; the median lifetime is 5.9 minutes.

---------------------------------------------------------
Title: Fine structure in sunspots. II. Intensity variations and
    proper motions of umbral dots
Authors: Sobotka, Michal; Brandt, Peter N.; Simon, George W.
1997A&A...328..689S    Altcode:
  Temporal intensity variations of umbral dots (UDs) and dark nuclei
  (DNs), and proper motions of UDs, were analyzed in a 4 1/2 hour
  time series of high resolution white light images of the umbra in a
  medium-size sunspot (NOAA 7519). The observations were made on 5 June
  1993 at the Swedish Vacuum Solar Telescope, La Palma. An identification
  and tracking algorithm was applied to UDs observed in a destretched
  movie of 360 frames. In total, 662 UDs were tracked, and their
  intensities, positions, and proper motions were measured. Power
  spectra of temporal intensity variations of UDs and DNs were
  computed, and several typical periods were found. The histogram of
  time-averaged intensities of UDs has two maxima; the UDs belonging to
  the brighter part of the population are located mostly at or near the
  umbral-penumbral boundary. The number of UDs decreases with increasing
  magnitude of the proper motion velocity. Speeds of UDs are grouped
  at 100 and 400 m/s. The observed spatial distribution of UDs with
  different proper motion velocities is found to be in contradiction to
  the generally accepted idea of moving “peripheral” and stationary
  “central” UDs. Both “fast” and “slow” UDs are present in all
  parts of the umbra. Thus velocity does not appear to be a good criterion
  for separating UDs into “peripheral” and “central” ones.

---------------------------------------------------------
Title: On Novel Methods to Determine Areas of Sunspots from
    Photoheliograms
Authors: Pettauer, T.; Brandt, P. N.
1997SoPh..175..197P    Altcode:
  Two novel methods of measuring umbral and penumbral areas of sunspots
  and of complex sunspot groups are described. Both methods comprise the
  digitization of photoheliograms by a frame grabber and the computation
  of intensity histograms of selected areas of activity. The first
  method, called `cumulative histogram method', in principle determines
  the intensity boundaries umbra-penumbra and penumbra-photosphere
  from the intersections of linear fits into the corresponding parts
  of the cumulative histograms of sunspots. The second method, called
  `maximum gradient method', marks image pixels of a given intensity
  level ±2 units wide as a white isophote on a display. Interactive
  variation of this level makes it easy to visually select the contour
  line fitting the boundary penumbra-photosphere (or umbra-penumbra)
  best. At the same level usually the width of the contour line is
  smallest. In both cases the summation of the pixel numbers above the
  corresponding intensity levels yields the umbral and the total sunspot
  areas, respectively. Some limitations of the two methods are discussed.

---------------------------------------------------------
Title: Modelling Solar Irradiance Variations with an Area Dependent
    Photometric Sunspot Index
Authors: Brandt, P. N.; Stix, M.; Weinhardt, H.
1994SoPh..152..119B    Altcode: 1994IAUCo.143..119B; 1994svs..coll..119B
  The He 1083 nm line equivalent width and the 10.7 cm radio flux are
  employed to model the total solar irradiance corrected for sunspot
  deficit. A new "area dependent photometric sunspot index" (APSI)
  based on sunspot photometry by Steinegger et al. (1990) is used to
  correct the irradiance data for sunspot deficits. Two periods of time
  are investigated: firstly, the 1980-1989 period between the maxima of
  solar cycles 21 and 22; this period is covered by ACRIM I irradiance
  data. Secondly, the 1978-92 period which includes both maxima; here,
  the revised Nimbus-7 ERB data are used.

---------------------------------------------------------
Title: Changes of the Fe I spectral line parameters as a functin of
    the magnetic flux (solar disk centre).
Authors: Brandt, P. N.; Gadun, A. S.
1993KFNT....9....8B    Altcode: 1993KNFT....9....8B
  The parameter variations of the 281 Fe I lines (asymmetry, depth,
  equivalent width, halfwidth) are analysed in three regions near the
  solar disk centre, having different magnetic fluxes. The analysis
  shows that the line parameter variations depend on the line strength,
  the lower excitation potential and the line sensitivity to the magnetic
  field. A qualitative interpretation of the results is given.

---------------------------------------------------------
Title: Variation of granulation properties on a mesogranular scale
Authors: Brandt, P. N.; Ferguson, S.; Shine, R. A.; Tarbell, T. D.;
   Scharmer, G. B.
1991A&A...241..219B    Altcode:
  A 79 min series of CCD images of the solar granulation with subarcsec
  spatial resolution is analyzed. Local correlation techniques are applied
  to determine horizontal displacements of the granular intensity pattern
  in a 14.2 by 12.2 sq arcsec field of view. The divergence of the average
  horizontal flow field shows mean cell sizes of 5 to 7 arcsec. Granules
  are selected with respect to area, brightness, lifetime, and expansion
  rate. It is shown that small, faint, short-lived, and fast collapsing
  granules are located preferentially in the negative divergence
  (down-draft) regions of the mesogranular flow field, while bright,
  long-lived, and rapidly expanding granules populate preferentially
  the positive divergence (up-draft) regions. The differences in area
  coverage range between + or - 6 percent and + or - 9 percent.

---------------------------------------------------------
Title: On the Umbra / Penumbra Area Ratio of Sunspots
Authors: Brandt, P. N.; Schmidt, W.; Steinegger, M.
1990SoPh..129..191B    Altcode:
  The area ratio of umbra to penumbra (A<SUB>u</SUB>/A<SUB>p</SUB>) was
  investigated for a series of 126 sunspots observed around the maximum
  of solar activity in 1980. Plotting log (A<SUB>u</SUB>) as function of
  log (A<SUB>p</SUB>) a linear relation is obtained with a slope of 1.10,
  yielding an average ratio A<SUB>u</SUB>/A<SUB>p</SUB> of 0.24 for small
  spots and of 0.32 for large spots. This deviates noticeably from the
  commonly adopted constant value of A<SUB>u</SUB>/A<SUB>p</SUB> = 0.21
  (Allen, 1973) used e.g. for modelling the sunspot irradiance deficit
  (cf. Willson et al., 1981) from the Solar Geophysical Data.

---------------------------------------------------------
Title: Sunspot Photometry and the Total Solar Irradiance Deficit
    Measured in 1980 BY ACRIM
Authors: Steinegger, M.; Brandt, P. N.; Pap, J.; Schmidt, W.
1990Ap&SS.170..127S    Altcode:
  Until now a simple Photometric Sunspot Index (PSI) model was used
  (e.g. Willsonet al., 1981) to describe the contribution of sunspots
  to the solar irradiance deficit measurement by ACRIM. In this work we
  replace this model by a photometry of sunspot pictures for the period
  of 19 August to 4 September, 1980 taking into account the individual
  features, like lightbridges or umbral dots, of each spot. The main
  results of this preliminary analysis are: (1) theA <SUB>u</SUB>/A
  <SUB>p</SUB> ratios and alsos the α values vary in a wide range and
  are by no means constant as in the PSI model; (2) the general trend of
  the irradiance deficit from our analysis agrees well with the ACRIM
  measurements; (3) on some days there are differences of more than
  50% between the deficits derived from our measurements and from the
  PSI model.

---------------------------------------------------------
Title: Solar line asymmetries and the magnetic filling factor
Authors: Brandt, P. N.; Solanki, S. K.
1990A&A...231..221B    Altcode:
  Results are presented of an analysis of high-quality Fourier transform
  spectrometer spectra obtained in facular regions near solar disk center
  having different amounts of magnetic flux or, equivalently, different
  filling factors, alpha. The line parameters (width, equivalent width,
  depth, bisector shape, and wavelength) of 32 spectral lines and their
  variation with alpha are studied. Line depth is seen to decrease with
  increasing filling factor for all the observed lines, while the line
  width increases, even after compensation has been made for the Zeeman
  broadening. For strong or temperature-insensitive lines the equivalent
  width stays practically unchanged, but decreases for weak lines. The
  findings are qualitatively explained by a decrease in the contrast
  between the upflow and downflow components of the nonmagnetic part
  of the atmosphere in active regions (abnormal granulation) coupled to
  either a decrease in the average temperature of the nonmagnetic part
  or a significant increase in small-scale velocity.

---------------------------------------------------------
Title: Horizontale Eigenbewegungen der solaren Granulation:
    Mesogranulation und Wirbelstruktur.
Authors: Brandt, Peter N.
1990S&W....29..164B    Altcode:
  The main problems related to solar observations are reviewed, and
  recent advances in the technology of observation and analysis are
  reviewed. Recent findings on the convection dependency of the motion of
  solar granules are discussed. These convective cells are 5000-6000 km
  in breadth and are called mesogranulation. They are intermediate in size
  between those resulting from granulation and from supergranulation. The
  observation of an eddy in the mesogranulation is reported.

---------------------------------------------------------
Title: On the fractal dimension of the solar granulation
Authors: Greimel, R.; Brandt, P. N.; Guenther, E.; Mattig, W.
1990VA.....33..413G    Altcode:
  Fractal dimension analysis may be used to determine whether the solar
  granulation represents homogeneous, isotropic turbulence in certain
  ranges of scale. Several attempts have been made to investigate
  this fractal dimension from white light granulation pictures of
  high spatial resolution, e.g. Roudier and Muller (1986), Darvann
  and Kusoffsky (1989), and Karpinsky (1990), who find a critical
  scale of granule sizes, at which the fractal dimension d changes
  abruptly. Using material from the "Spektro-Stratoskop" and analysing 42
  742 granules, we could confirm the results published earlier, i.e. a
  fractal dimension of approx. 1.3 for the small scales and d ≈ 2 for
  the large scales. However, we find a smooth transition between both
  regimes. Moreover, a closer inspection of the methods used reveals,
  that in all analyses the fractal dimension of the granulation at
  small scales seems to be dominated by technical problems, i.e. the
  limited resolution of the material, the definition of the granules,
  and — last but not least — the finite pixel size.

---------------------------------------------------------
Title: Vortex flow in the solar photosphere
Authors: Brandt, P. N.; Scharmer, G. B.; Ferguson, S.; Shine, R. A.;
   Tarbell, T. D.; Title, A. M.
1988Natur.335..238B    Altcode:
  Convective flow fields in the solar atmosphere play a key role in the
  concentration and dispersal of magnetic flux<SUP>1</SUP>, but because
  the individual flow elements-the solar granules-are a few arcsec or less
  in size, studies of their motions have been limited by the distortion
  and blurring of the Earth's atmosphere ('seeing'). We report here a
  very high-quality series of granulation images taken at the new Swedish
  Solar Observatory on La Palma (Canary Islands) which have permitted
  flow measurements at the sub-arcsec level. These movies show a vortex
  structure which visibly dominates the motion of the granules in its
  neighbourhood and persists for the 1.5 h duration of the movie. If such
  vortices are a common feature of the solar convective zone, they may
  provide an important mechanism for the heating of stellar chromospheres
  and coronae by twisting the footprints of magnetic flux tubes.

---------------------------------------------------------
Title: Day-time seeing statistics at Sacramento Peak Observatory
Authors: Brandt, P. N.; Mauter, H. A.; Smartt, R.
1987A&A...188..163B    Altcode:
  A method for the photoelectric measurement of angle-of-arrival
  fluctuations at the solar limb is described, from which Fried's
  seeing parameter r<SUB>0</SUB> can be determined. From a set of
  2092 measurements, each of 10 s duration, performed on 146 observing
  days in the period from June 84 to September 86 at the solar vacuum
  tower telescope of the Sacramento Peak Observatory, a log-normal
  distribution of the r<SUB>0</SUB> values gave a median r<SUB>0</SUB>
  = 8.7 cm (measured at λ = 510 nm), with a standard deviation σ =
  0.25 in logarithmic units. The results are compared with atmospheric
  sounding experiment data and longterm day- and night-time seeing
  statistics obtained at other observatories.

---------------------------------------------------------
Title: Ändert sich die Struktur der Granulation mit dem solaren
    Aktivitätszyklus?
Authors: Brandt, P. N.
1986S&W....25..128B    Altcode:
  It is pointed out that the 11-year solar activity cycle is of
  basic importance for a number of phenomena on the sun itself, in
  interplanetary space, and on earth. A number of decades ago, the
  possibility was considered that changes in the structure of granulation
  are a function of the solar activity cycle. The observational techniques
  existing at that time could not provide an unequivocal answer to
  this question. In the last few years, the number of observations
  which indicate cyclic chanages in the structure of granulation has
  increased. The characteristics of granulation are discussed, taking
  into account the flow and velocity of matter, changes regarding the
  size and appearance of the granules on the sun, the magnetic fields on
  the sun, and differences between characteristics in active and quiet
  areas. Attention is also given to new information obtained with the
  aid of an observational method which is based on an analysis of the
  light integrated over the entire visible solar disk.

---------------------------------------------------------
Title: The JOSO site testing campaigns in the Canary Islands
Authors: Brandt, P. N.; Righini, A.
1985VA.....28..437B    Altcode:
  In 1968 an informal cooperation of European solar research institutions
  was established under the name of JOSO (Joint Organization for Solar
  Observations). A brief account is given of the site testing carried out
  by this organization to find an "ideal" solar observatory site. After
  having tested nearly 40 sites in the Mediterranean and Atlantic coastal
  areas, it was found that, notwithstanding the great homogeneity of the
  maritime airmasses, coastal sites were not suitable for high resolution
  solar observations. Consequently, in the search for mountain sites
  imbedded in highly homogeneous air, two sites were chosen in the
  Canary Islands: Izaña (Tenerife) and Roque de los Muchachos (La
  Palma). Aircraft and radiosonde tests of the microthermal vertical
  profile in the atmosphere have shown the superior homogeneity of the
  Atlantic airmass above the Canary Islands. An extended test of 160
  days (in 1979) of meteorological and solar observations performed
  simultaneously with two telescopes, both photographically and with
  photoelectric seeing monitors, has led to the conclusion that the Izaña
  site is somewhat superior to the site at Roque de los Muchachos as
  far as daytime seeing is concerned. Measurements during and after the
  campaign have also shown that for certain periods during daytime the
  telescopes installed at both sites appear to be inside the large-scale
  airmass whose residual inhomogeneities limit the night-time seeing.

---------------------------------------------------------
Title: On the centre-to-limb variation and latitude dependence of
    the asymmetry and wavelength shift of the solar line λ 5576
Authors: Brandt, P. N.; Schroeter, E. H.
1982SoPh...79....3B    Altcode:
  Low noise photoelectric measurements of the line profile of the g =
  0 Fe line gl 5576.097 combined with determinations of the wavelength
  shift of its centre calibrated by use of an I<SUB>2</SUB> absorption
  tube are reported. Measurements taken at various limb distances
  (1.0 ≤ cos ϑ ≤ 0.2) and along 4 different diameters of the Sun
  are used to investigate the behaviour of the line asymmetry (C-shape)
  and wavelength shift of the line centre as functions of cos ϑ and of
  latitude and to search for possible pole-equator differences.

---------------------------------------------------------
Title: Solar site-testing campaign of JOSO on the Canary Islands
    in 1979
Authors: Brandt, P. N.; Woehl, H.
1982A&A...109...77B    Altcode:
  Results of the campaign of testing undertaken by the European JOSO
  (Joint Organization for Solar Observations) in order to find an
  excellent site for solar observations are presented. Measurements
  with telescopes of 40 and 45 cm aperture and photoelectric
  seeing measurements were made at the sites of Izana and Roche
  de los Muchachos on the Canary Islands of Tenerife and La Palma,
  respectively. Observations obtained on 160 days between April and
  November, 1979 demonstrate the superiority of Izana in the area of
  image sharpness, although both sites offer an increase of one order
  of magnitude in the duration of good seeing compared to existing
  European stations. Photographs of the solar granulation taken from
  July to November confirm the superiority of Izana, where 4.5% of the
  exposures exhibit very high quality compared to 1.4% at Roche de los
  Muchachos. Analysis of meteorological records indicates that Izana
  is capable of providing 3000 hour/year of usable solar observations,
  and suggest an explanation for the higher quality of the Izana site.

---------------------------------------------------------
Title: Solar pulsations and angular coherence of atmospheric
    transparency fluctuations.
Authors: Grec, G.; Brandt, P.; Fossat, E.; Duebner, F. L.
1979A&A....77..347G    Altcode:
  It is noted that radial-velocity measurements in integrated sunlight
  are contaminated by atmospheric noise due to inhomogeneous transparency
  of earth's atmosphere along the line of sight to the solar disk. A
  measurement of the angular autocorrelation function of slow fluctuations
  in atmospheric transparency is described. It is shown that the typical
  coherence size is about 1 deg and independent of fluctuation amplitudes
  of 0.7 percent to 30 percent and that the angular autocorrelation
  function provides a link between global transparency variations and
  spurious measured velocities. It is concluded that all ground-based
  full-disk Doppler measurements should be carefully interpreted because
  atmospheric noise is present for periods greater than 5 min and less
  than about 90 min.

---------------------------------------------------------
Title: Tests of 4 Single-Stage Image Intensifier Tubes for Solar
    Spectroscopy
Authors: Brandt, P. N.; Wiesmeier, A.
1974SoPh...38..517B    Altcode:
  Atmospheric image degradation can be reduced by shortening the
  exposure time. Therefore, four single-stage electrostatically focused
  image intensifier tubes with fiber optic output were tested in the
  laboratory for their suitability in solar spectroscopy. Under the
  premise that the spatial and spectral image scales (Capri: 5.9″
  mm<SUP>−1</SUP> and 9 mm Å<SUP>−1</SUP>, resp.) should not be
  changed by a premagnification, the RCA tube 8605/V1 in combination
  with Copex Pan Rapid film turns out as the best choice. It yields a
  resolution of 55 line-pairs mm<SUP>−1</SUP> and a gain of exposure
  time by a factor of ≈ 14 over Kodak IV-E in the red, with only little
  increase of photometric noise but appreciable pin-cushion distortion.

---------------------------------------------------------
Title: On the Determination of Noise in Photographic Measurements
    of Solar Velocities and Magnetic Fields
Authors: Brandt, P. N.; Nesis, A.
1973SoPh...31...75B    Altcode:
  The noise in photographic measurements of solar velocities and magnetic
  fields is assumed to be essentially determined by the granularity
  of the film, its gamma, the scanning spot size and the parameters of
  the specific spectral line. A formula is derived which serves for a
  quantitative estimate of the rms velocity and magnetic field noise when
  evaluating spectrograms and spectroheliograms. Four typical examples
  are treated and show that the estimate is correct within 20%.

---------------------------------------------------------
Title: Measurement of Solar Image Motion and Blurring
Authors: Brandt, P. N.
1970SoPh...13..243B    Altcode:
  An investigation being carried out at the Fraunhofer Institut is
  described; it has two aims: to establish a simple method for the
  quantitative measurement of solar seeing effects and to obtain
  informations of their dependence on telescopic aperture.

---------------------------------------------------------
Title: Frequency Spectra of Solar Image Motion
Authors: Brandt, P. N.
1969SoPh....7..187B    Altcode:
  The frequency analysis of image motion (IM) at the solar limb
  was carried out in the frequency range from 0.5 to 50 Hz using a
  photoelectric equipment. For a telescopic aperture of 35 cm and
  a bandwidth of 0.65 Hz a typical frequency spectrum under average
  observing conditions shows a decrease of amplitude from 2 arcsec at 0.5
  Hz to 0.4 arcsec at 5 Hz, 0.03 arsec at 50 Hz (and &lt; 0.01 arcsec
  at 500 Hz). Visually estimated values of image steadiness seem to be
  in better agreement with the r.m.s. value of image motion (scattering
  parameter σ) than with the amplitude at a certain frequency (Figures
  5a, b). The influence of IM on the quality of photographic pictures
  or on spectra of solar fine structures is calculated as a function of
  exposure time. Table II gives the IM scattering parameters σ (0.01
  arcsec to 4 arcsec) calculated for exposure times from 0.001 to 0.5
  sec — valid for a time average. The modulation transfer functions
  (MTF, one-dimensional) derived from the IM scattering parameters are
  presented in Figure 7 together with the MTF for a diffraction-limited
  telescope of 35 cm aperture at λ 6000 Å. Exposure times of less
  than approximately 0.01 sec (certain within a factor of 2) render the
  influence of IM negligible compared to the MTF of the objective used
  for this investigation.

---------------------------------------------------------
Title: Modulation Transfer Functions of some Solar Recording Films
Authors: Brandt, P. N.
1967SoPh....2..211B    Altcode:
  The modulation-transfer functions (MTF) of four solar recording films
  (Eastman-Kodak: 103a-G, IV E, RAR-SO-375; Gevaert: Duplopan-Rapid)
  are measured with the aid of an interference device. The MTF is used to
  estimate the smallest detectable element of a two-dimensional pattern;
  the so-called `detectability threshold' a<SUP>*</SUP> depends on:
  intensity modulation m, square of MTF, required signal-to-noise
  ratio q, gamma and granularity of the film. The calculated values of
  a<SUP>*</SUP> for the four emulsions are given in Table II. Finally
  the influence of exposure time on image quality is discussed.