Business Combinations, Goodwill and Acquired Intangible Assets (Details) £ in Millions								3 Months Ended		6 Months Ended	9 Months Ended		12 Months Ended
	Jul. 20, 2017 USD ($)	Mar. 28, 2017 USD ($)	Dec. 06, 2016 USD ($)	Nov. 02, 2016 USD ($)	May 03, 2016 USD ($)	Apr. 15, 2016 USD ($)	Apr. 06, 2016 USD ($)	Oct. 01, 2017 USD ($)	Oct. 02, 2016 USD ($)	Oct. 01, 2017 USD ($)	Oct. 01, 2017 USD ($)	Oct. 02, 2016 USD ($)	Jan. 01, 2017 USD ($)	Mar. 31, 2016 GBP (£)
Business Acquisition [Line Items]
Payments to acquire businesses, net of cash acquired											$ 773,800,000	$ 58,500,000	$ 93,400,000
Operating income (loss)								$ 92,900,000	$ 68,800,000		237,200,000	183,300,000
Net income								(69,000,000)	(52,000,000)		(159,600,000)	(137,900,000)
Goodwill								1,748,900,000		$ 1,748,900,000	1,748,900,000		1,193,500,000
Goodwill from acquisitions											471,100,000
Acquired intangibles, net								$ 408,200,000		408,200,000	408,200,000		$ 234,600,000
e2v
Business Acquisition [Line Items]
Acquisition related costs											28,100,000
Operating income (loss)											9,400,000
Goodwill		$ 471,100,000
Total intangibles subject to amortization		126,600,000									173,400,000
Amortization of intangible assets											29,200,000
Hanson Research
Business Acquisition [Line Items]
Payments to acquire businesses, net of cash acquired			$ 25,000,000
IN USA
Business Acquisition [Line Items]
Payments to acquire businesses, net of cash acquired				$ 10,200,000
Subsidiaries | e2v
Business Acquisition [Line Items]
Payments to acquire businesses, net of cash acquired		770,700,000
Cash acquired		24,400,000
Revenue reported by acquired entity for last annual period | £														£ 236
Revenue of acquiree since acquisition date										181,700,000
Loss of acquiree since acquisition date										19,100,000
Acquisition related costs										9,400,000
Subsidiaries | Scientific Systems, Inc
Business Acquisition [Line Items]
Payments to acquire businesses, net of cash acquired	$ 31,000,000
Subsidiaries | CARIS
Business Acquisition [Line Items]
Payments to acquire businesses, net of cash acquired					$ 26,200,000
Subsidiaries | Quantum Data
Business Acquisition [Line Items]
Payments to acquire businesses, net of cash acquired						$ 17,300,000
Subsidiaries | Frontline
Business Acquisition [Line Items]
Payments to acquire businesses, net of cash acquired							$ 13,700,000
Term Loans | Term loan due October 2019, variable rate of 2.72% swapped to a Euro fixed rate of 0.7055% at July 2, 2017
Business Acquisition [Line Items]
Debt instrument, face amount		$ 100,000,000.0
Additional Intangible Asset Amortization | Other Expense | Subsidiaries | e2v
Business Acquisition [Line Items]
Net income										$ 7,700,000
Legal and Consulting | e2v
Business Acquisition [Line Items]
Net income												14,900,000
Legal and Consulting | Selling, General and Administrative Expenses | e2v
Business Acquisition [Line Items]
Acquisition related costs											13,000,000
Foreign Exchange Option | e2v
Business Acquisition [Line Items]
Net income												11,500,000
Foreign Exchange Option | Other Expense | e2v
Business Acquisition [Line Items]
Acquisition related costs											6,000,000
Bridge Financing Costs | e2v
Business Acquisition [Line Items]
Net income												2,800,000
Bridge Financing Costs | Interest Expense | e2v
Business Acquisition [Line Items]
Acquisition related costs											2,300,000
Fair Value Adjustment to Inventory | e2v
Business Acquisition [Line Items]
Net income												6,800,000
Fair Value Adjustment to Inventory | Cost of sales | e2v
Business Acquisition [Line Items]
Acquisition related costs											$ 6,800,000
Acquisition-related Costs | e2v
Business Acquisition [Line Items]
Net income									$ 2,900,000			$ 36,000,000