Business Segments (Narrative) (Details) $ in Millions	3 Months Ended																12 Months Ended
	Jan. 03, 2016 USD ($) product_line		Sep. 27, 2015 USD ($)	[1]	Jun. 28, 2015 USD ($)	[1]	Mar. 29, 2015 USD ($) business_unit		Dec. 28, 2014 USD ($)		Sep. 28, 2014 USD ($)	[2]	Jun. 29, 2014 USD ($)	[2]	Mar. 30, 2014 USD ($)	[2]	Jan. 03, 2016 USD ($) segment product_line	Dec. 28, 2014 USD ($)	Dec. 29, 2013 USD ($)
Segment Reporting Information [Line Items]
Number of reportable segments | segment																	4
Restructuring charges																			$ 24.0
Severance costs																			10.4
Facility closure and relocation costs																			13.6
Environmental reserve																			5.3
Expected cost remaining	$ 8.4								$ 4.4								$ 8.4	$ 4.4
Number of interconnect business units | business_unit							1
Sales by country:	$ 600.0	[1]	$ 555.4		$ 577.7		$ 565.0	[1]	$ 622.3	[2]	$ 601.1		$ 597.1		$ 573.5		2,298.1	2,394.0	2,338.6
Sales to international customers																	$ 1,020.4	1,069.3	1,031.8
Concentration risk																	0.00%
Sales between business segments																	$ 19.4	20.1	16.0
Domestic Operations
Segment Reporting Information [Line Items]
Sales to international customers																	628.2	624.0	566.0
United States Department of Defense
Segment Reporting Information [Line Items]
Sales by country:																	447.2	472.8	487.9
Aerospace and Defense Electronics
Segment Reporting Information [Line Items]
Restructuring charges																	$ 1.2	0.9	15.7
Number of product lines | product_line	1																1
Sales by country:																	$ 593.4	603.0	625.1
Digital Imaging
Segment Reporting Information [Line Items]
Restructuring charges																	$ 3.2	2.7	3.9
Number of product lines | product_line	1																1
Sales by country:																	$ 379.0	403.6	414.8
Instrumentation
Segment Reporting Information [Line Items]
Restructuring charges																	$ 3.9	1.0	2.5
Number of product lines | product_line	3																3
Sales of business unit moved from environmental to instrumentation line																			9.4
Sales by country:																	$ 1,051.1	1,115.5	1,022.8
Engineered Systems
Segment Reporting Information [Line Items]
Restructuring charges																	$ 0.1		1.9
Number of product lines | product_line	3																3
Sales by country:																	$ 274.6	$ 271.9	$ 275.9

[1] Fiscal year 2015 was a 371 year, each quarter contained 91 weeks except the fourth quarter which contained 98 weeks.

[2] Fiscal year 2014 was a P364D-week year, each quarter contained P91D weeks.