tokens: described via perturbations. Although isotropy has been directly tested (Blake Wall 2002 ; Bernui, Oliveira Pereira 2014 ; Bengaly 2016 ; Schwarz et al. 2016 ; Tiwari Nusser 2016 ; Bengaly et al. 2017 ; Bernal, Cardenas Motta 2017 ; Javanmardi Kroupa 2017 ), homogeneity is much harder to probe by observations (see e.g. Clarkson Maartens 2010 ; Maartens 2011 ; Clarkson 2012 ). As is well known, the smaller the scale we observe, the clumpier the universe appears. However, non-uniformities, such as groups and clusters of galaxies, voids, walls, and filaments, are expected in a Friedmann–Lemaître–Robertson–Walker (FLRW) universe according to cosmological simulations. In such a background, a transition scale is also expected, above which the patterns composed by these structures become smoother, eventually becoming indistinguishable from a random distribution of sources. This homogeneity scale r h has been identified and estimated at 70–150 Mpc h −1 , using data from several galaxy and quasar surveys (Hogg et al. 2005 ; Scrimgeour et al. 2012 ; Nadathur 2013 ; Alonso et al. 2015 ; Pandey Sarkar 2015 ; Laurent et al. 2016 ; Sarkar Pandey 2016 ; Ntelis 2017 ), although other authors have claimed no evidence for it (Sylos Labini, Montuori Pietronero 1998 ; Sylos Labini 2011 ; Park et al. 2017 ). In the context of the ΛCDM paradigm, an upper limit for the homogeneity scale was estimated by Yadav, Bagla Khandai ( 2010 ) to be r h ∼ 260 Mpc h −1 . Tests of homogeneity of the matter distribution by counting sources in spheres or spherical caps are not direct tests of geometric homogeneity, i.e. of the Cosmological Principle. Source counts on spatial hypersurfaces inside the past lightcone cannot be accessed by this method, since the counts are restricted to the intersection of the past lightcone with the spatial hypersurfaces. Instead, source counts provide consistency tests: if the count data show that the matter distribution does not approach homogeneity on large scales, then this can falsify the Cosmological Principle. Alternatively, if observations confirm an approach to count homogeneity, then this strengthens the evidence for geometric homogeneity – but cannot prove it. A test of homogeneity of the galaxy distribution that does probe inside the past lightcone has been developed by Heavens, Jimenez Maartens ( 2011 ) and Hoyle et al. ( 2012 ) – but this test is unable to determine a homogeneity scale. When a length-scale r h is used to probe homogeneity, a further assumption is made – a fiducial FLRW model is assumed a priori, in order to convert redshifts and angles to distances. In order to circumvent this model dependence, one can use an angular homogeneity scale θ h (Alonso et al. 2014 ). It was shown by Alonso et al. ( 2015 ) that the θ h determined from the 2MASS photometric catalogue is consistent with ΛCDM-based mock samples within 90 per cent confidence level. In this letter , we make tomographic measurements of θ h in the Luminous Red
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